Friday, 19 November 2021

Mr Greedy and the Tale of the Minimum Tracking Error Variance - Part two

My last blog post was about a new method for a daily dynamic optimisation of portfolios with limited capital, to allow them to trade large numbers of instruments. 

(Although I normally write my blog posts to be self contained, you'll definitely have to read the previous one for this to make any sense!)

Subsequent to writing that post I implemented the method, and quickly ran into some problems. Basically the dammn thing was trading too much. Fortunately there is a single parameter which controls trading speed in the model - the shadow cost. I turned up the shadow cost to a very high value and spent a few days investigating what had went wrong.

Broadly speaking, I found that:

  • My measure of turnover wasn't suitable for 'sparse' portfolios, i.e. portfolios where most instruments have a zero position at any given time
  • My measure of risk adjusted costs also wasn't suitable
  • The true turnover of the dynamic optimised portfolio was much higher than I'd realised
  • The true trading costs were thus also much higher
  • Thus the results in my previous post were misleading and wrong

After discussing with Doug (the original source of this idea) I realised I'd been missing a step: postion buffering. This is something I did in my original static system to slow down my trading behaviour, but which was missing here. 

In this post I explain:

  • Some other bad things I did
  • Why my approximations for trading costs and turnover were wrong, and how I fixed them
  • Why increasing the shadow cost doesn't help
  • Why position buffering is a good thing and how it works in the old 'static' system
  • How to create a position buffering method for dynamic optimisation
  • How I calibrated the position buffering and shadow cost for the dynamic model
  • How I used shrinkage to make the results more stable
  • A more appropriate benchmark
  • Some revised results using the new method, and more accurate statistics

So there's a lot there, but this has been quite an extensive (and at times painful!) piece of research.


Some other bad things I did


As well as the stuff I've already mentioned I did some bad things when implementing the model to production. I was so excited about the concept, basically I rushed it. Here's a list of things I did:

  • Not thinking more carefully about the interpretation of the shadow cost
  • Not using common code between sim and production (this didn't serious cause problems, but did make it harder to work out what was going ong)
  • Not paper trading for long enough
I ought to know better, so this just goes to show that even supposedly experienced and smart people make mistakes...



My (bad) approximations for trading costs and turnover


I'm a big fan of using risk adjusted measures for trading costs and other things. Here's how I used to work out trading costs:

  • Work out the current cost of trading
  • Divide that by current vol to calculate the cost in SR units
  • Calculate the turnover in contracts
  • Calculate the normalised turnover; dividing the historic turnover in contracts by the current average position, and the taking an average
  • The average position assumes we have a constant forecast of +10
  • Multiply the normalised turnover
  • I do a similar calculation for rolling costs, assuming I roll an average position worth of contracts N times a year (where N is the number of rolls each year)
The big flaw in this, with respect to sparse positions, is the average position. Clearly our average position is going to be much smaller than we think, which means our turnover will look unnaturally low, and our costs unrealistically low.

  • Work out the current cost of trading in actual $$$ terms
  • For each historic trade, multiply that by the number of contracts traded
  • For rolling costs, assume we roll a number of contracts equal to the number of contracts we held in the period before the roll (gives a more reliable figure)
  • Deflate these figures according to the difference in price volatility between then and now
  • So for example, if the vol of S&P 500 is 20% with a price of 5000, that's a price vol of 1000
  • If that figure was 200 at some point in the past, then we'd divide the historic cost by 5
This still risk adjusts costs, but in such a way that it will reflect sparse positions.

(Incidentally, I still use the old SR based method to calculate the cost of a trading rule, for which we don't really know the exact number of contracts)

We don't use turnover anymore, but it would still be nice to know what it is. It's hard to calculate a turnover per instrument with sparse positions, but we can meaningfully calculate the turnover for an entire system. We do this by calculating the turnover in contracts at the portfolio level (after dynamic optimisation, or after buffering for the static system), divide each of these by the expected average position (assuming a forecast of +10, and accounting for instrument weights and IDM), and then add these up. 


Why shadow cost doesn't help - much


So when I first calculated this new measure of average turnover for the dynamic system, it was quite a bit higher than I expected.

"No problem" I thought "I'll increase the shadow cost".

Remember the shadow cost is a multiplier on the cost penalty applied to the dynamic optimisation. Increasing it ought to slow the system down.

And it does... but not by as much as I'd hoped, and with a decreasing effect for higher shadow costs. Digging under the hood of the greedy algo, the reason for this is that the algo always starts at zero (in the absence of corner case constraints) and then starts changing position with the sign of the optimal unrounded position

So it will always end up with the same sign of position as the underlying optimal position. To put it another way, every time the underlying forecast changes sign, we'll definitely trade regardless of the size of the shadow cost. All the shadow cost will do is reduce trading in instruments where we haven't seen a sign change.

No biggie, except for the uber-portfolio I was running in production with over 110 instruments. Let's say their average holding period is a conservative two months; so they change sign roughly every 42 business days. That means on any given day we'd see around three instruments changing sign, and trading. This imposes a lower limit on turnover, no matter how much you crank up the shadow cost. 

There isn't a lot you can do about this, except perhaps switch to a different optimisation method. I did look at this, but I really like the intuitive behaviour of the greedy algo.

Another - smaller - effect is that the more instruments you have, the higher your IDM, the higher your turnover will be (as a rule of thumb, if you double your leverage on an individual instrument, you'll also double your turnover).

So it's important to do any testing with a sufficiently large portfolio of instruments relative to capital.


Position buffering in a static system


Anyway the solution, after discussion with Doug, revolves around something in my old 'static' system that's missing from the new dynamic system: position buffering. 

Doug isn't doing exactly what I've decided to do, but the principal of applying a buffer was his idea so is due credit

Position buffering works something like this; suppose we calculate an optimal (unrounded) position of long +2.3 contracts (2 contracts rounded). We then measure a buffer around this; which for the sake of argument we'll say is 2 contracts wide. So the position plus buffer will be (lower level) 1.3 contracts to (upper level) 3.3 contracts. Rounded that's +1 to +3 contracts. 

We then compare this to our current position. If that's between 1 and 3, we're good. We do nothing. However let's suppose our current position is +4 contracts. Then we'd sell... not 2 contracts bringing us back to the (rounded) optimal of +2, but instead a single contract to bring us to +3... the edge of the buffer.

Buffering reduces our turnover without affecting our performance, as long as the buffer isn't too wide. Calibrating the exact width of the buffer is quite involved (it's related to the interplay of forecast speed and costs for a given instrument), so I've always used a simple 10% of average position (the position I'd get with an average forecast of +10).


Position buffering in a dynamic system


How do we impose a buffer on the dynamic system? We could try and set up the optimisation so it treats all positions within the buffer for each instrument as having the same utility... but that would be darned messy. And as we're not doing a grid search which tests every possible integer contract holding we wouldn't neccesarily use the buffer in a sensible way.

Instead we need to do the buffering at a portfolio level. And we'll do the buffering on our utility function: the tracking error.

So the basic idea is this: if the tracking error of the current portfolio is less than some buffer level, we'll stick with the current portfolio (='inside the buffer'). If it isn't, we'll trade in such a way to bring our tracking error down to the buffered level (='trading to the edge of the buffer').

We actually do this as a three step process. In step one we calculate the tracking error of the current portfolio, versus the portfolio with unrounded optimal positions (let's call this tracking error /unrounded). If this is less than the buffer, we stick with the current positions. No optimisation is needed. This step doesn't affect what happens next, except to speed things up by reducing the number of times we need to do a full blown optimisation.

Step two: we do the optimisation, which gives a portfolio consisting of integer positions. Step three: we now calculate a second tracking error: the tracking error of the currently held portfolio versus the integer positions (tracking error/rounded). By construction, this tracking error will be lower than tracking error/unrounded. 

We now calculate an adjustment factor, which is a function of tracking error/rounded (which I'm now going to rename x) and the buffer (b):

Adjustment factor = max((x - b)/x, 0)

We then multiply all our required trades (from current to integer optimised) by the adjustment factor. And then round them, obviously.

So if the tracking error is less than the buffer, we don't trade. Otherwise we do a proportion of the required trade. The further away we are from the buffer, the more of the trade we'll do. For a very large x, we'd do almost all of our trade.

Note that (ignoring the fact we need to round trades) doing this will bring our tracking error back to the edge of the buffer.



Calibrating buffer size and shadow cost


Note the buffer doesn't replace the shadow cost; it's in addition to it. The shadow cost is handy since it penalises the costs of trading according to the different costs of each instrument. Nevertheless, both methods will slow down our trading so we have to consider their joint effect.

We could do this with an old school, in sample, grid search of parameters. Instead let's use some common sense.

Firstly, with an average target risk of 25%, a 10% buffer around that means our dynamic buffer size should be around 1.25% (not 2.5% as you might expect as this buffer is expressed differently).

Now consider the shadow cost. In my prior post I said that a shadow cost of 10 'looked about right', but a few moments thought reveals it is not. Remember the utility function is tracking error - costs. Tracking error is measured in units of annualised standard deviation. How much does a tracking error of 1% lose use in terms of expected return? Difficult to say, but let's make some assumptions:

  • Sharpe Ratio 1.0
  • Target annual standard deviation 25%
  • Target annual return = 1.0 * 25% = 25%
  • Suppose we're running at half the risk we want, so our tracking error will be 12.5%
  • In this case we'll also be missing out on ~12.5% of annual return
  • If SR = 1, then tracking error is effectively in annualised return units
Now bear in mind the utility function subtracts the cost from a given optimisation; which is probably a daily cost, we need to annualise this. So a shadow cost of 250 would annualise costs and put them in the same units as the tracking error.

To recap then:

- Shadow cost 250
- Buffer size 0.0125


Shrinkage and the mystery of the non semi-definite matrix


In the discussion 'below the line' of the previous post it was suggested that the turnover in the correlation matrix might be responsible for the additional costs. Basically, if the correlation estimate was to change enough it would cause the optimal portfolio to change a lot as well.

It was suggested to try shrinking the correlation matrix, which would result in fewer correlation changes. But the correlation estimate is also quite slow so I didn't shrinkage would be worthwhile. However I then discovered another problem, which led me down quite the rabbit hole. 

Essentially, once I started examining the results of my optimisation more carefully, I realised that for large (100+ instrument) portfolios there were instances when my optimisation just broke as it couldn't evaluate the utility function. One cause was inputting costs of nan, and was easily fixed by making my cost deflation function more accurate. But I also got errors trying to find the standard deviation of the tracking error portfolio. 

So it turns out that pandas doesn't actually guarantee to produce positive semi-definite correlation matrices, which means that sometimes the tracking error of the portfolio can have a negative variance. I experimented with trying to find the nearest PSD matrix - it's very slow, too slow for backtesting though possibly worth a last line of defence. I tried tweaking the parameters of the exponential correlation; even tried going back to vanilla non exponential correlation estimates but still ended up with non PSD matrices. 

What eventually came to the rescue, just as I was about to give up, was shrinking the correlation matrix. For reasons that are too boring to go into here (but try here), shrinkage is a good way of fixing PSD issues. And shrinking the correlation matrix in this particular application isn't really a bad thing. It makes it less likely we'll put on weird positions, just because correlations are especially high or low.

(If anyone has come across this problem with pandas, and has a solution, I'd like to hear it...)


How should we assess this change?


Yet another flaw in the previous post was an excessive reliance on looking at Sharpe Ratios to see if performance improved, comparing a plain 'rounded' with an optimised portfolio. 

However, there is an element of luck involved here. For example, if there was an instrument with a low contract size which still had positions even for a small unoptimised portfolio, and which had a higher SR than anything else, then the simple rounded portfolio would outperform the optimised portfolio. 

A better set of metrics would be:
  • The correlation in returns between an unrounded and the rounded optimised portfolio
  • The level of costs paid in SR units
  • The total portfolio level turnover (see notes above)
We'd want to check the SR wasn't completely massacred by the dynamic optimisation, but a slight fall in SR isn't a go/no go decision.



The static benchmark

It could be argued that a better benchmark would not be the simple rounded static portfolio with say 100 instruments; but instead the 30 or so instrument static portfolio you'd actually be able to trade with say $500K in your account. Again, there is an element of luck here, depending on which set of 30 or so instruments you choose. But it would give a good indication of what sort of turnover we are aiming for, and whether we had the costs about right.

So I reran the process described here, and came up with the following list of static instruments for a $500K portfolio:

instrument_list = ['DOW', 'MUMMY','FTSECHINAA', 'OAT',  'NIFTY', 'KOSDAQ','SP500_micro', 'NIKKEI',
'BOBL', 'KR10','KR3','EDOLLAR', 'US10U','US3',
'SOYOIL',
'WHEAT', 'LIVECOW', 'LEANHOG',
'CNH', 'YENEUR','RUR','BRE', 'JPY', 'MXP', 'NZD','CHF',
'BITCOIN', 'IRON','SILVER', 'GOLD_micro' ,
'CRUDE_W_mini', 'GASOILINE','GAS_US_mini',
'VIX'
]
Notice I've grouped these by asset class:
  • Equities
  • Bonds/STIR
  • Ags
  • Currencies
  • Metals
  • Energies
  • Vol
The results are different from last time, as I've added more instruments to my data set, and also excluded some instruments which are too expensive / illiquid; having spent some time recently on putting together a systematic process for identifying those.

For benchmarking purposes I allowed the instrument weights to be fitted in both dynamic and static cases, however both sets of portfolios have forecast weights that are fitted in sample for speed.


Results versus benchmark


First let's get a feel for the set of instruments we are playing with. We have 114 instruments in total, reflecting my constantly expanding universe, with data history that looks like this:

For the 34 instruments in the benchmark portfolio, it's worth bearing in mind that prior to 2000 we have less than 15 instruments, and so the early part of the backtest might be worth a pinch or two of salt:




Now in reality we can't hold 114 instruments at once, so in the dynamic optimised portfolio we end up holding around a quarter to a third of what's available on any given day:


Whilst in the benchmark portfolio we mostly hold positions in around 90-100% of what we can trade:

Let's dig into the optimiser some more and make sure it's doing it's job. Here is the position series for the S&P 500 micro. The blue line shows the position we'd have on without rounding. Naturally the green buffered position follows this quite closely. We actually end up with the orange line after optimisation; it follows along but at times clearly prefers to get it's risk from elsewhere. This is a cheap future so the turnover is relatively high:

Another plot I used in the previous post was to see how closely the expected risk tracked between the unrouded and optimised portfolio. It's still a very close match:
Remember one of our key metrics was the return correlation between the unrounded and optimised portfolios. This comes in at a very unshabby 0.986.

Let's look at some summary statistics. The Sharpe Ratio of the optimised portfolio is 1.336 gross, 1.287 net. So that's a SR cost loss of ~5bp a year. In other words, we'd expect to lose 1/20 of our vol target (1/20 of 25% = 1.25%) in costs annually; the actual average cost is 1.7% a year. The portfolio level turnover is 51.1 times a year. 

In comparison the benchmark portfolio hits a Sharpe Ratio of gross 1.322, net 1.275, SR in costs again ~5bp. Actual average cost is slightly lower at 1.45% a year. Turnover is 37.5. I'll discuss those figures in more detail later.

Incidentally, the (unachievable!) Sharpe Ratio of the unrounded portfolio with 114 instruments is 1.359. So we're only losing a few bp in SR when holding about a quarter to a third of the available instruments. You can see how close the account curves are here:
Orange: Unrounded, Blue: Optimised

Another way of visualising the costs: If I plot the costs with the sign flipped, and multiplied by 10, and then add on the net account curve; you can see how we are losing less than half  (so less than 5%) of our gross performance. Also the compounded costs are steady and linear, indicating a nice consistency over time.

Let's compare that to the benchmark:


Although the proportion of costs is slightly lower, you can see here that costs have increased over time. And in fact the annual costs over the last 15 years have been around 2%: higher than the 1.7% achieved by the dynamic system. 

So if we're comparing dynamic with static benchmark:

  • In recent years it has lower costs
  • But probably higher turnover
  • The historic net Sharpe Ratio is effectively identical

The turnover isn't a massive deal, as long as we have accurately estimated our trading costs: we'll do a few more trades, but on average they will be in cheaper markets.

However, to reiterate, the results of the static system are very much more a matter of luck in market selection particularly for the early backtest when it only has a few markets. Overall I'd still rather have the dynamic system - with the opportunity to catch market movements in over 100 markets and counting - than the static system where if I am missing a market that happens to move I will kick myself.


Summary

"I've prodded and poked this methodology in backtesting, and I'm fairly confident it's working well and does what I expect it to." ....

.... is something I wrote in my last post. And I was wrong! However, after a lot more prodding and poking, which has had the side effect of tightening up a lot of my backtesting framework and making me think a lot, I'm now much more confident. And indeed this system is now trading 'live'.

That was the seventh post on the best way to trade futures with a small account size, and - barring another unexpected problem - that's all folks!




Friday, 1 October 2021

Mr Greedy and the Tale of the Minimum Tracking Error Variance [optimising portfolios for small accounts dynamic optimisation testing / yet another method!]

 This is the sixth (!) post in a (loosely defined) series about finding the best way to trade futures with a relatively small account size.

  • This first (old) post, which wasn't conciously part of a series, uses an 'ugly hack': a non linear rescaling of forecasts such that we only take positions for relatively large forecast size. This is the method I was using for many years.
  • These two posts (first and second) discuss an idea for dynamic optmisation of positions. Which doesn't work.
  • This post discusses a static optimisation method for selecting the best set of instruments to include in a system given limited capital. This works! This is the method I've been using more recently.
  • Finally, in the last post I go back to dynamic optimisation, but this time using a simpler heuristic method. Again, this didn't work very well.
(Incidentally, if you're new to this problem, it's probably worth reading the first post on dynamic optimisation post in my series

That would be the end of the story, apart from the fact that I got a mysterious twitter reply:


After some back and forth I finally got round to chatting to Doug in mid September. Afterwards, Doug sent me over some code, which was in R, a language I haven't used for 14 years but I did manage to translate it into Python and then integrate it into https://github.com/robcarver17/pysystemtrade, and added in some variations of my own (more realistic costs, and some constraints for use in live trading). Then I tested it. And blimey, it actually bloody worked.


UPDATE (22nd October 2021) 

It didn't work, at least not as well as I'd hoped.

After writing this post and implementing the idea in production I found some issues in my backtesting results were producing misleading results (in short my cost calculations were not appropriate for a system with 'sparse' positions - there is more detail here). 

I could rewrite this post, but I think it's better to leave it as a monument to my inadequacy. I'm working on an alternative version of this method that I hope will work better.


What was Doug's brilliant idea


Doug's idea had two main insights:
  • It's far more stable to minimise the variance of the tracking error portfolio, rather than using my original idea (maximising the utility of the target portfolio, having extracted the expected return from the optimal portfolio). And indeed this is a well known technique in quant finance (people who run index funds are forever minimising tracking error variance).
  • A grid search is unneccessary given that in portfolio optimisation we usually have a lot of very similar portfolios, all of which are equally as good, and finding the global optimum doesn't usually give us much value. So using a greedy algorithm is a sufficiently good search method, and also a lot faster as it doesn't require exponentially more time as we add assets.

Mr Greedy
https://mrmen.fandom.com/wiki/Mr._Greedy?file=Mr_greedy_1A.png



Here's the core code (well my version of Doug's R code to be precise):

def greedy_algo_across_integer_values(
obj_instance: objectiveFunctionForGreedy
) -> np.array:

## Starting weights
## These will eithier be all zero, or in the presence of constraints will include the minima
weight_start = obj_instance.starting_weights_as_np()

## Evaluate the starting weights. We're minimising here
best_value = obj_instance.evaluate(weight_start)
best_solution = weight_start

done = False

while not done:
new_best_value, new_solution = _find_possible_new_best(best_solution = best_solution,
best_value=best_value,
obj_instance=obj_instance)

if new_best_value<best_value:
# reached a new optimium (we're minimising remember)
best_value = new_best_value
best_solution = new_solution
else:
# we can't do any better (or we're in a local minima, but such is greedy algorithim life)
break

return best_solution


def _find_possible_new_best(best_solution: np.array,
best_value: float,
obj_instance: objectiveFunctionForGreedy) -> tuple:

new_best_value = best_value
new_solution = best_solution

per_contract_value = obj_instance.per_contract_value_as_np
direction = obj_instance.direction_as_np

count_assets = len(best_solution)
for i in range(count_assets):
temp_step = copy(best_solution)
temp_step[i] = temp_step[i] + per_contract_value[i] * direction[i]

temp_objective_value = obj_instance.evaluate(temp_step)
if temp_objective_value < new_best_value:
new_best_value = temp_objective_value
new_solution = temp_step

return new_best_value, new_solution

Hopefully that's pretty clear and obvious. A couple of important notes:

  • The direction will always be the sign of the optimal position. So we'd normally start at zero (start_weights), and then get gradually longer (if the optimal is positive), or start at zero and get gradually shorter (if the optimal position is a negative short). This means we're only ever moving in one direction which makes the greedy algorithim work. Note: This is different with certain corner cases in the presence of constraints. See the end of the post.
  • We move in steps of per_contract_value. Since everything is being done in portfolio weights space (eg 150% means the notional value of our position is equal to 1.5 times our capital: see the first post for more detail), not contract space, these won't be integers; and the per_contract_value will be different for each instrument we're trading.

Let's have a little look at the objective function (the interesting bit, not the boilerplate). Here 'weights_optimal_as_np' are the fractional weights we'd want to take if we could trade fractional contracts:


class objectiveFunctionForGreedy:
    ....
def evaluate(self, weights: np.array) -> float:
solution_gap = weights - self.weights_optimal_as_np
track_error = \
(solution_gap.dot(self.covariance_matrix_as_np).dot(solution_gap))**.5

trade_costs = self.calculate_costs(weights)

return track_error + trade_costs

def calculate_costs(self, weights: np.array) -> float:
if self.no_prior_weights_provided:
return 0.0
trade_gap = weights - self.weights_prior_as_np
costs_per_trade = self.costs_as_np
trade_costs = sum(abs(costs_per_trade * trade_gap * self.trade_shadow_cost))

return trade_costs

The tracking error portfolio is just the portfolio whose weights are the gap between our current weights and the optimal unrounded weights, and what we are trying to minimise is the standard deviation of that portfolio.

The covariance matrix used to calculate the standard deviation is the one for instrument returns (not trading subsystem returns); if you've followed the story you will recall that I spent some time grappling with this decision before and I see no reason to change my mind.  For this particular methodology the use of instrument returns is a complete no-brainer.

The shadow cost is required because portfolio standard deviation and trading costs are in completely different units, so we can't just add them together. It defaults to 10 in my code (some experimentation reveals roughly this value gives the same turnover as the original system before the optimisation occurs. As you'll see later I haven't optimised this for performance).



Performance


And let's have a look at some results (45 instruments, $100K in capital). All systems are using the same basic 3 momentum crossover+carry rules I introduce in chapter 15 of my first book.



So if we were able to take fractional positions (which we're not!) we could make the green line (which has a Sharpe Ratio of 1.17). But we can't take fractional positions! (sad face and a Sharpe Ratio of just 1.06). But if we run the optimiser, we can achieve the blue line, even without requiring fractional positions. Which has a Sharpe Ratio of .... drumroll... 1.19. 

Costs? About 0.13 SR units for all three versions.

Tiny differences in Sharpe Ratio aside, the optimisation process does a great job in getting pretty close to the raw unrounded portfolio (correlation of returns 0.94). OK the rounded portfolio is even more correlated (0.97) , but I think that's a price worth paying.

That's a little higher than what you will have seen in previous backtests. The reason is I'm now including holding costs in my calculations. I plan to exclude some instruments from trading whose holding costs are a little high, which will bring these figures down, but for now I've left them in.

If I do a t-test comparing the returns of the three account curves I find that the optimised version is indistinguishable from the unrounded fractional position version. And I also find that the optimised version is significantly better than the rounded positions: a T-statistic of 3.7 with a tiny p-value. Since these are the versions we can actually run in practice, that is a stonking win for the optimisation.


Risk


The interesting thing about the greedy algorithm is that it gradually adds risk until it finds the optimal position, whilst trying to reduce the variance of the delta portfolio, so it should hopefully target similar risk. Here is the expected (ex-ante) risk for all three systems:

Red line: original system with rounded positions, Green line: original system with unrounded positions, Blue line: optimised system with unrounded positions


It's quite hard to see what's going on there, so let's zoom into more recent data:


You can see that the optimiser does a superb job of targeting the required risk, compared to the systematically under-risked (in this period - sometimes it will be over-risked) and lumpy risk presented by the rounded positions. The ex-post risk over the entire dataset comes in at 22.4% (unrounded), 20.9% (rounded) and 21.6% (optimised); versus a target of 20%. 


How many positions do we typically take?


An interesting question that Doug asked me is how many positions the optimiser typically takes.

"Curious how many positions it uses of the 45??

I guess I don’t know how much capital you are running, but given there are really only maybe 10 independent bets there (or not many more) does it find a parsimonious answer that you might use even if you had a giant portfolio to run?"

Remember we have 45 markets we could choose from in this setup, how many do we actually use?

Blue line: Total number of instruments with data. Orange line: Instruments with positions from optimiser


The answer is, not many! The average is 6, and the maximum is 18; mostly it's less than 12. And (apart from at the very beginning) the number of instruments chosen hasn't increased as we add more possible instruments to our portfolio. Of course we couldn't really run our system with just 12 instruments, since the 12 instruments we're using varies from period to period. But as Doug notes (in an email):

"Pretty cool. The dimension of the returns just isn’t all that high even though there are so many things moving around." 

Interestingly, here are some statistics showing the % of time any given instrument has a position on. I've done this over the last 7 years, as otherwise it would be biased towards instruments for which we have far more data:

PALLAD          0.00
COPPER          0.00
GASOILINE       0.00
FEEDCOW         0.00
PLAT            0.00
HEATOIL         0.00
GBP             0.01
REDWHEAT        0.02
WHEAT           0.02
EUR             0.02
NZD             0.03
CRUDE_W_mini    0.03
US20            0.03
US10            0.03
SOYOIL          0.04
LEANHOG         0.04
AUD             0.04
LIVECOW         0.05
JPY             0.05
SOYMEAL         0.06
CAC             0.07
SOYBEAN         0.08
OATIES          0.08
OAT             0.09
RICE            0.10
US5             0.11
MXP             0.12
CORN            0.13
BTP             0.14
SMI             0.14
AEX             0.14
GOLD_micro      0.19
EUROSTX         0.23
KR10            0.24
BITCOIN         0.26
EU-DIV30        0.33
BUND            0.39
EDOLLAR         0.39
BOBL            0.43
NASDAQ_micro    0.47
VIX             0.55
SP500_micro     0.60
KR3             0.66
US2             0.73
SHATZ           0.74


Notice we end up taking positions in all but six instruments. And even if we never take a position in those instruments, their signals are still contributing to the information we have about other markets. Remember from the previous posts, I may want to include instruments in the optimisation that are too illiquid or expensive to trade, and then subsequently not take positions in them.

I've highlighted in bold the 16 instruments we trade the most. You might want to take the approach of only trading these instruments: effectively ignoring the dynamic nature of the optimisation and saying 'This is a portfolio that mostly reproduces the exposure I want'. 

However notice that they're all financial instruments (Gold and Bitcoin, quasi financial), reflecting that the big trends of the last 7 years have all been financial. So we'd probably want to go further back. Here are the instruments with the most positions over all the data:

PLAT            0.24
RICE            0.25
CRUDE_W_mini    0.26
NASDAQ_micro    0.27
SOYMEAL         0.33
US2             0.35
US5             0.38
WHEAT           0.39
LIVECOW         0.40
LEANHOG         0.41
CORN            0.43
SOYOIL          0.44
EDOLLAR         0.46
SP500_micro     0.56
GOLD_micro      0.56
OATIES          0.61

That's a much more diversified set of instruments. But I still don't think this is the way forward.


Tracking error


Tracking error: I like to think of as quantified regret. Regret that you're missing out on trends in markets you don't have a full size position in...

What does the tracking error look like? Here are the differences in daily returns between the unrounded and optimised portfolio:

The standard deviation is 0.486%. It also looks like the tracking error has grown a little over time, but 2020 aside it has been fairly steady for a number of years. My hunch is that as we get more markets in the dataset it becomes more likely that we'll have fractional positions in a lot of markets that the optimiser can't match very well. And indeed, if I plot the tracking error of rounded versus unrounded portfolios, it shows a similar pattern. The standard deviation for that tracking error is also virtually identical: 0.494%. 



Checking the cost effects


It's worth checking to see what effect the cost penalty is having. I had a quick look at Eurodollar, since we know from the above analysis that it's a market we normally have a position on. Zooming in to recent history to make things clearer:




The green line is the unrounded position we'd ideally want to have on, wheras the red line shows our simple rounded (and buffered) position. The blue line shows what the optimiser would do without a cost penalty. It trades - a lot! And the orange line shows our optimised position. It's trading a bit more than the red line, and interestingly often has a larger position on (where it's probably taking on more of the load of being long fixed income from other instruments), but it's definitely trading a lot less than the blue line.

Interestingly the addition of the cost penalty doesn't reduce backtested costs much, and reduces net performance a little: about 1 SR point, but I'd still rather have the penalty thanks very much. 



Much lower capital

To ssee how robust this approach is, let's repeat some of the analysis above with just 50K in capital. 




So the optimised version is still better than the rounded (SR improvement around 0.1), but nowhere near as good as the unrounded (SR penalty around 0.2). We can't work miracles! With 50K we just don't have enough capital to accurately reflect the exposures we'd like to take in 45 markets. The tracking error vs the unrounded portfolio is 0.72% for the optimiser (versus 0.49% earlier with 100K), but is even higher for the rounded portfolio (0.76%). The correlation between the optimiser and ideal unrounded optimal returns has dropped to 0.86 (0.94 with 100K); but for rounded positions is even lower: 0.84 (0.97 with 100K).

Less capital makes it harder to match the unrounded position of a large portfolio of instruments, but relatively speaking the dynamic optimisation is still the superior method.

Important note: With 


What does this mean?

Let's just review what our options are if we have limited capital, of say $100K:
  • We could win the lottery and trade the unrounded positions.
  • We could try and trade a lot of instruments - say 45 - and just let our positions be rounded. This gives us a SR penalty of around 0.1 SR versus what we could do with unrounded positions. The penalty would be larger (in expectation) with less capital and / or more instruments (eg it's 0.3SR with 50k). The tracking error would also get larger for smaller capital, relative to the number of instruments.
  • We could try and choose a set of static instruments and just trade those. In this post I showed that we could probably choose 16 instruments using a systematic approach. This would also give us a SR penalty of around 0.1 SR in expectation, but the tracking error would be larger than for rounded positions. Again with less capital / more instruments both penalties and tracking error would be larger.
  • We could use the 'principal components' approach, to choose a static list of the 16 instruments that are normally selected by the optimiser. I've highlighted these in the list of instruments above. Our tracking error would be a little smaller (in expectation) than for rounded positions, but we'd still have a SR penalty of around 0.1 SR.
  • We could have as many instruments as we liked in our portfolio and use the dynamic optimisation approach to decide which of those to hold positions for today. Normally this means we'll only have positions in around 10 instruments or so, but the 10 involved will change from day to day. Our tracking error would be similar as for rounded positions, but we'd not be giving up much in terms of SR (if anything). With smaller capital or more instruments we'd get some SR penalty (but less than the alternatives), and higher tracking error (but again better than the alternatives). 
Ignoring the first option, it strikes me that dynamic optimisation brings significant benefits, which for me overcome the additional complexity it introduces into our trading.


Live trading


If you're clever, you will have noticed that the algo code above doesn't include any provision for some of the features I specified in my initital post on this subject:

  • A 'reduce only' constraint, so I can gradually remove instruments which no longer meet liquidity and cost requirements
  • A 'do not trade' constraint, if for some reason 
  • Maximum position constraints (which could be for any reason really) 
The psystemtrade version of the code here covers these possibilities. It adjusts the starting weights and direction depending on the constraints above, and also introduces minima and maxima into the optimisation (and prevents the greedy algorithim from adjusting weights any further once they've hit those). It's a bit complicated because there are quite a few corner cases to deal with, but hopefully it makes sense.

Note: I could use a more exhaustive grid search for live trading, which only optimises once a day, but I wouldn't be able to backtest it with 100+ instruments so I'll stick with the greedy algorithim, which also has the virtue of being a very robust and stable process and avoids duplicating code.

Let's have a play with this code and see how well it works. Here's what the optimised positions are for a particular day in the data. In the first column is the portfolio weight per contract. The previous days portfolio weights are shown in the next column. The third column shows the optimal portfolio weights we'd have in the absence of rounding. The optimised positions are in the final column. I've sorted by optimal position, and removed some very small weights for clarity:

              per contract  previous  optimal  optimised
SHATZ 1.32 -10.56 -3.08 -5.27
BOBL 1.59 -1.59 -1.09 0.00
OAT 1.97 0.00 -0.31 0.00
VIX 0.24 0.00 -0.14 -0.24
EUR 1.47 0.00 -0.13 0.00
... snip...

GOLD_micro 0.18 0.00 -0.01 -0.18
... snip...

AEX 1.84 1.86 0.12 0.00
EUROSTX 0.48 0.00 0.13 0.48
EU-DIV30 0.22 0.22 0.14 0.00
MXP 0.25 0.00 0.16 0.00
US10 1.33 1.33 0.17 1.33
SMI 1.27 0.00 0.19 0.00
SP500_micro 0.22 0.00 0.21 0.00
US20 1.64 0.00 0.23 0.00
NASDAQ_micro 0.30 0.31 0.26 0.30
US5 1.23 2.47 0.33 2.47
KR10 1.07 0.00 0.41 0.00
BUND 2.01 0.00 0.91 0.00
EDOLLAR 2.47 0.00 1.44 0.00
KR3 0.94 3.77 2.96 3.77
US2 2.20 8.81 17.44 8.81

Now let's suppose we could only take a single contract position in US 5 year bonds, which is a maximum portfolio weight of 1.23:

              weight per contract  previous  optimal  optimised  with no trade
SHATZ 1.32 -10.56 -3.08 -5.27 -2.63
BOBL 1.59 -1.59 -1.09 0.00 0.00
OAT 1.97 0.00 -0.31 0.00 0.00
VIX 0.24 0.00 -0.14 -0.24 -0.24
... snip...
GOLD_micro                   0.18      0.00    -0.01      -0.18           0.00
... snip...
AEX                          1.84      1.86     0.12       0.00           0.00
EUROSTX 0.48 0.00 0.13 0.48 0.48
EU-DIV30 0.22 0.22 0.14 0.00 0.00
MXP 0.25 0.00 0.16 0.00 0.00
US10 1.33 1.33 0.17 1.33 1.33
SMI 1.27 0.00 0.19 0.00 0.00
SP500_micro 0.22 0.00 0.21 0.00 0.00
US20 1.64 0.00 0.23 0.00 0.00
NASDAQ_micro 0.30 0.31 0.26 0.30 0.30
US5 1.23 2.47 0.33 2.47 1.23
KR10 1.07 0.00 0.41 0.00 0.00
BUND 2.01 0.00 0.91 0.00 0.00
EDOLLAR 2.47 0.00 1.44 0.00 0.00
KR3 0.94 3.77 2.96 3.77 3.77
US2 2.20 8.81 17.44 8.81 8.81
That works. Notice that to compensate we reduce our short in two correlated market (German 2 year bonds and Gold, both of which have correlations above 0.55); for some reason this is a better option that increasing our long position elsewhere.

Now suppose we can't currently trade German 5 year bonds, Bobls, (but we remove the position constraint):

              weight per contract  previous  optimal  optimised  with no trade
SHATZ 1.32 -10.56 -3.08 -5.27 -2.63
BOBL 1.59 -1.59 -1.09 0.00 -1.59
OAT 1.97 0.00 -0.31 0.00 0.00
VIX 0.24 0.00 -0.14 -0.24 -0.24
... snip...
GOLD_micro                   0.18      0.00    -0.01      -0.18          -0.18
... snip ...
AEX                          1.84      1.86     0.12       0.00           0.00
EUROSTX 0.48 0.00 0.13 0.48 0.48
EU-DIV30 0.22 0.22 0.14 0.00 0.00
MXP 0.25 0.00 0.16 0.00 0.00
US10 1.33 1.33 0.17 1.33 2.66
SMI 1.27 0.00 0.19 0.00 0.00
SP500_micro 0.22 0.00 0.21 0.00 0.00
US20 1.64 0.00 0.23 0.00 0.00
NASDAQ_micro 0.30 0.31 0.26 0.30 0.30
US5 1.23 2.47 0.33 2.47 1.23
KR10 1.07 0.00 0.41 0.00 0.00
BUND 2.01 0.00 0.91 0.00 0.00
EDOLLAR 2.47 0.00 1.44 0.00 0.00
KR3 0.94 3.77 2.96 3.77 3.77
US2 2.20 8.81 17.44 8.81 8.81
Our position in Bobl remains the same, and to compensate for the extra short we go less short 2 year Shatz, longer 10 year German bonds (Bunds), and there is also some action in US 5 year and 10 year bonds.

Finally consider a case when we can only reduce our position. There are a limited number of markets where this will do anything in this example, so let's do it with Gold and Eurostoxx (which the previous day have zero position, so this will be equivalent to not trading)

                weight per contract  previous  optimal  optimised  reduce only
SHATZ 1.32 -10.56 -3.08 -5.27 -5.27
BOBL 1.59 -1.59 -1.09 0.00 0.00
OAT 1.97 0.00 -0.31 0.00 0.00
VIX 0.24 0.00 -0.14 -0.24 -0.24
EUR 1.47 0.00 -0.13 0.00 0.00
... snip ...
GOLD_micro                   0.18      0.00    -0.01      -0.18         0.00
... snip ...
EUROSTX                      0.48      0.00     0.13       0.48         0.00
EU-DIV30 0.22 0.22 0.14 0.00 0.22
MXP 0.25 0.00 0.16 0.00 0.00
US10 1.33 1.33 0.17 1.33 1.33
SMI 1.27 0.00 0.19 0.00 0.00
SP500_micro 0.22 0.00 0.21 0.00 0.22
US20 1.64 0.00 0.23 0.00 0.00
NASDAQ_micro 0.30 0.31 0.26 0.30 0.30
US5 1.23 2.47 0.33 2.47 1.23
KR10 1.07 0.00 0.41 0.00 0.00
BUND 2.01 0.00 0.91 0.00 0.00
EDOLLAR 2.47 0.00 1.44 0.00 0.00
KR3 0.94 3.77 2.96 3.77 3.77
US2 2.20 8.81 17.44 8.81 8.81

Once again the exposure we can't take in Eurostoxx is pushed elsewhere: into EU-DIV30 (another European equity index) and S&P 500; the fact we can't go as short in Gold is compensated for by a slightly smaller long in US5 year bonds.


What's next


I've prodded and poked this methodology in backtesting, and I'm fairly confident it's working well and does what I expect it to. The next step is to write an order generation layer (the bit of code that basically takes optimal positions and current live positions, and issues orders: that will replace the current layer, which just does buffering), and develop some additional diagnostic reports for live trading (the sort of dataframes in the section above would work well, to get a feel for how maxima and minima are affecting the results). I'll then create a paper trading system which will include the 100+ instruments I currently have data for. 

At some point I'll be ready to switch my live trading to this new system. The nice thing about the methodology is that it will gradually transition out of whatever positions I happen to have on into the optimal positions, so there won't be a 'cliff edge' effect of changing systems (I might impose a temporarily higher shadow cost to make this process even smoother).

In the mean time, if anyone has any ideas for further diagnostics that I can run to test this idea out I'd be happy to hear them.

Finally I'd like to thank Doug once again for his valuable insight. 



Monday, 6 September 2021

Truth and Liebor

 This will be a bit different from my normal posts. It's basically some personal reflections on the LIBOR fixing scandal, prompted by having just read this book written by Stelios Contogoulas





This post isn't really a book review, although I will say that the book is definitely worth buying. Most of you have probably already read the excellent Spider Network. That is arguably better written than Stelios' book (as it's written by a professional journalist, and as anyone who has read my books knows ex-traders are not always naturally gifted writers - Nassim Taleb is a black swan in this respect). Stelios' book is less polished, but he still does a good job of hooking you into the narrative and it got very exciting towards the end.

More importantly, as far as I am aware Stelios is the only person who has written a book about this scandal from the inside. And his book is very thoughtful and reflective, and his reflection has inspired some personal thoughts of my own.



Three traders


This post is about three people. One of them is Stelios. Another is an Italian by the name of Carlo Palombo. And the third is me.


Stelios


Carlo


Me


What do we have in common? Well, we're all in our forties, and our hair has long since departed our scalps. But more importantly we were all trading interest rate derivatives at Barclays Capital (as the investment banking arm of Barclays bank was known at the time) at the same time: from around September 2002 to February 2004 (when I left the bank). 

In fact until early 2004 the life and career of myself and Stelios followed an eerily similar track. Stelios of course grew up in Greece not England and is three years older than I am, but like me he lived abroad as an expat child. Like me he was interested in computers, and like me he decided a career in IT was not for him (in my case I dropped out after my first year at University, in his case after several years in IT consulting).

We both returned to education a little later in life, attending the University of Manchester at the same time. I was a mature Economics undergraduate, whilst Stelios was doing an MBA. We overlapped by about 18 months but we probably never met, although many of our lectures would have been in the same building.

Stelios was hired by Barclays in early 2002 as an associate after doing an internship (at the same time as I was doing an internship at AHL). When I was being interviewed for a position on the Barclays analyst programme, he had probably just started in the Canary Wharf office (5 North Colonnade - the home of Barclays investment bank then, and now, at least until next year). We were interviewed by some of the same people, a few months apart. 

We were both hired, I suspect, for ulterior motives. Stelios' computing experience meant that he didn't start properly trading for a couple of years, as he was initially tasked with rebuilding the banks yield curve systems. My instinct is that I was hired because I had the right personality and was a few years older than the other graduates - more of that in a second.

In September 2002 I started on the graduate programme. The programme covered around 75 analysts and associates, covering back, middle and front office. I was one of only two traders. The other was Carlo Palombo. 



Derivatives trading at Barclays


Stelios and Carlo were working within a few metres of each other, both working on the interest rate swaps desk (which also traded FRAs). I was on the next bank of desks, but no more than 10 metres from each of them. My job was a little fancier; at least in theory. I was working on the exotics rates desk, which confusingly covered both vanilla options (swaptions, caps and floors) as well as actual exotics (bermudans, CMS, PRDMC...). However like Stelios and Carlo I was very much a junior trader.

My line manager was the desk MD, a very smart and decent guy who looked like a bouncer. But I reported day to day to the desk's senior trader, who ran the main vega book (options maturing in over a year; there was also a gamma book for shorter options which I eventually took over, plus various traders trading FX, caps/floors, inflation; and we also had an on desk quant / trader for the very fancy stuff). 

A thinly disguised version of this bloke appears in my first book ('Sergei'). He was an extremely unpleasant person to work for. I suspect I was hired - despite not having the Phd everyone else on the desk had - because it was thought with a few years of work experience I would be able to deal with this character better than a 21 year old neophyte or fresh faced Phd. It sort of worked - at least for me; I didn't end up being a glorified coffee boy like most junior traders as I refused to take any crap.

But Carlo was reporting to a guy called Jay (who traded the short Euro swaps and FRAs), who made my senior trader look like an social worker.  He really gave Carlo hell, and the poor guy practically cowered under the tirade of abuse he got if he made even the slightest error. I felt sorry for Carlo, as I was working relatively relaxed hours (7am to 5pm), much less than the other analysts on the IB programme, and also a lot less than Carlo who practically had to sleep under his desk to keep up with the workload. Interestingly in Stelios' book he refers to Jay as:

 '... very demanding as a person- particularly with juniors - but when he liked someone, he was a great manager and mentor'. 

OK. Maybe I just didn't see his good side - perhaps he didn't like me or need to like me, or maybe I'm just a snowflake who was too soft to work on the trading floor. I certainly couldn't have worked on the swaps desk which was much larger than ours, and always seemed to have at least five people yelling abuse at each other. 

Outside of business I knew Carlo reasonably well as there were often nights at the pub or house parties with the other members of the grad programme, but I probably only spoke to Stelios half a dozen times during my time at Barclays. 



The crucial post it note


We didn't have a huge amount of interaction with 'the delta desk' as we disparagingly called the swaps traders, although we were supposed to do our hedging with them internally, and we also used to occasionally get them to clear up the fixing risk on our books. Sometimes a complex deal would need co-ordination between the desks, but mostly we had a friendly(ish) distant rivalry. We thought the delta traders were a bit simple (how hard could it be to trade swaps and FRAs, compared to bermudan swaptions?), and they probably thought we were a bit lazy and arrogant. As a junior trader from the stuck up exotics desk I tried to avoid the very scary looking senior swaps traders like Jay wherever possible.

One day however we had some large expiries in our book, and the market price was very close to the strike. 

About 15 minutes before the expiry (and fixing time) 'Sergei' leant over to me and in an uncharacteristically quiet voice said 

"Go tell X that we have a large expiry on this morning". 'X' was a senior swaps trader

'Oh come on, don't make me walk over there. Why don't I just message or call him' I moaned, not fancying running the gauntlet of the swaps desk.

'Don't be so f***** stupid. Go over and tell him, face to face.' hissed Sergei in reply. I rolled my eyes.

'For f**** sake' he muttered, and grabbed a post it note 'Just do it. Here is the expiry we have on. I've written it down so you don't forget it. Make sure you get it right. And make sure you bring that post-it note right back here'

Now I was intruiged. This was more like a spy mission than the normal humdrum business of trading. I wandered over to X (who fortunately was one of the nicer blokes on the swaps desk), and passed the crucial information on.

'We have this expiry today' I said, and read off the post it note. X nodded sagely but said nothing. I stood there for a few moments, not sure exactly what was supposed to happen next. He turned back to his screen, which was obviously my cue to leave. 

I returned to my desk, and sat down. Sergei held out his hand without looking at me.

'Post it note' he snapped. I pulled the scrap of yellow paper out of the pocket I had stuffed it into, and passed it over. I watched as he methodically tore it into tiny pieces, and then put the pieces into his own pocket. Then he turned to me and winked. Belatedly, I realised what had just happened.

Some background information, swaptions (options on swaps) were mostly cash settled against something which you can think of as a bit like a 'Swap Libor' fixing. Like LIBOR it was calculated daily from an average of figures given by a panel of banks. The swaps desk was resposible for submitting their estimated figures of where swaps were trading at a specific time each morning.

Note here the direct analogy with LIBOR:

The swaptions desk will gain / lose if swaps fix in a particular place
-   The swaps desk will gain / lose if LIBOR fixes in a particular place
The swaptions desk are not responsible for submitting the swap fix - the swaps desk are
-   The swaps desk are not responsible for submitting the LIBOR fix - the cash desk are
To influence the swap fix the swaptions desk will have to speak to the swaps desk
-    To influence the LIBOR fix the swap desk will have to speak to the cash desk

Now, I am not saying that Sergei was trying to influence the swaps fix that day in favour of our expiry. And indeed, the message I had passed on was not 'We'd like the fix to be higher today please' All I had told X was the position that we had on. Of course, X could have easily inferred where we would like the fix to be. And he could have used that to change the rate he submitted. 

All in all, it seemed a bit fishy. If this was kosher, why the secrecy? Why didn't Sergei want any electronic or taped record of my conversation with X to exist? Why had he torn up the post it note, and even been careful enough not to put it in the bin by his desk, but presumably take it home for more secure disposal? 

To be clear: I didn't even have the slightest thought that it might be illegal; nothing like this had been covered in eithier my regulatory exams or in the training the bank had provided. And I'd had no formal training whatsoever on the swap fix, or even the expiry process. Still it was definitely a step beyond my own moral boundaries I turned to Sergei and said as confidently as I could:

'I'd rather not do that again if it's okay with you'

He looked at me and smirked. 'Whatever. Now see if you can find a broker to buy us some lunch. I fancy some Ubon today.'

I felt like I'd failed some kind of test, but whatever he thought I was never asked again. In case you're wondering, I don't remember there being anything 'weird' about the expiry today, nor do I remember if we ended up in a profitable position. I have no idea whatsoever if X did anything at all, or if he was just being polite and pretending to do us a favour. 

And, for what it's worth, I never saw any evidence that any further requests were made by Sergei or anyone else. Perhaps he was just very discreet, perhaps it was a very rare event which I just happened to be part of, or perhaps I'd shocked him into a more virtous life (although that seems unlikely). 
 

What I did next


Over the next few months there were other things that seemed fishy to me, but I couldn't avoid doing most of them. One of them I have talked about for several years now, here, in the newspapers, to the UK parliament, and on TV: the practice of selling embedded derivatives to local authorities and housing associations as part of 'LOBO' loans.

Importantly, there was nothing secretive about the LOBO business: communication was done properly over recorded lines, and there were no post it notes bandied around. I remember only one exception, which I described in my earlier blog post:

"On this particular deal the commission was so large in percentage terms that it exceeded internal limits. Even the most hard nosed traders on the trading desk were feeling pangs of.... well not guilt perhaps but fear that this kind of thing might one day be written on a blog. But the broker agreed to take half of the commission spread over subsequent deals, so that was okay."

For that trade there was indeed a lot of whispering, and the real commission was never written down or discussed in a recorded setting - not even on a post it note (it might have been written in biro on someones hand). 

Again it was clear to me that was going on was definitely immoral, but I never even considered it might be illegal. And of course, no court has ever found that Barclays (or any other bank) were engaged in illegal activity in relation to the LOBO deals and there has been no regulatory action. But the banks have 'voluntarily' agreed to 'tear up' many of the LOBO deals and replace with straightforward loans, often taking significant mark to market losses in the process. 

(I remember going to a compulsory course on ethics at Barclays where they told us not to do anything that could end up on the front page of the newspaper, even if it was legal. That amused me no end when I was quoted on the front page of the FT in reference to the LOBO scandal).

The morally grey activities and the stress of working on the sell side all got a bit much for me.  I decided in Febuary 2004 to leave Barclays. My MD tried to make me stay; he even broke the rules and told me what my year end bonus would me if I stayed at least until April. I pointed out that I was probably giving up a lot more money in the long run, but this wasn't for me, and I wasn't entirely happy with a lot of the stuff we were doing.

You know the rest if you've followed my blog; I did a couple of years at an economics think tank and then joined AHL in 2006 where I lived happily every after (at least until 2013, when I left and now live happily ever after writing stuff for you guys to read). 


What Stelios and Carlo did next


What happened to Stelios and Carlo? Well they both stayed at Barclays, and not long after I left Stelios was allowed to begin trading properly, initially on the sterling FRA book, then subsequently covering USD short end swaps for the London desk. And at some point, both were asked to pass on requests to cash desks to ensure LIBOR and/or EURIBOR fixes reflected their trading book.

It's worth quoting from Stelios' book:

"One morning, Fred stood up from his chair...  'Come with me, there's someone I want you to meet'

The two of us walked a few rows away on the edge of the trading floor... Sitting there was Peter Johnson... He was an Englishman in his early fifties with already a long career at Barclays. He was an established, succesful, and very senior trader.

'Stelios this is Peter....' said Fred 'He is the US cash trader here at Barclays and he's the person responsibile for submitting LIBOR rates for the bank. Alex and I will be asking you on occasion to relay some information to him, relating to LIBOR rates and our preference on it. So, all you have to do is to let him know, OK?'

Peter got up... 'Nice to meet you, Stelios. Just let me know whenever you boys need something and I'll do my best to help out' he said."

And thus the die was cast.


The LIBOR scandal


When the rumours about LIBOR first surfaced in 2008 (and ironically, I think it was Tim Bond from Barclays who brought 'lowballing' to everyones attention), I immediately remember the incident from five years earlier. My first thought was 'Yes, that's absolutely what would have been happening', and then 'Wait, is that really illegal?'. 

The rest is history not worth repeating here; but for Stelios and Carlo it did not end well, as both were prosecuted for LIBOR and EURIBOR fixing respectively.  I won't tell you what happened to Stelios, you can google it if you like or better still read his book. Sadly, Carlo was sentenced to four years in prison, and could be there until 2023 (although hopefully he will qualify for an earlier release).

Several other traders were also found guilty, of which the most high profile was certainly Tom Hayes who was finally released a few months ago.


Why them, and not me?


I'm not going to discuss the rights and wrongs of the scandal here, I'm not going to debate as to whether any law was actually broken; nor will I tell you how I feel that only relatively junior people got prosectuted whilst their bosses got away with murder. You can read Stelios' book, as he's basically in broad agreement with me on all of these issues.

But there is one point I want to finish with. In Stelios' book he includes this line:

"Try to put yourself in my shoes and think about how you would have acted in my place"

For me this is especially poignant. It really could have been me. I wasn't actually in Stelios' shoes, but I was standing (or rather sitting) just a few metres away. And yet I acted quite differently.

I'd like to think that it's because I have an especially finely tuned moral compass, but if I'm being brutally honest I'm not sure that's the case (and to be fair to Stelios, in my limited personal dealings with him, and in his book, he comes across as a pretty decent guy).

Realistically, if I was in Stelios' shoes, or Carlo's for that matter, I probably would have done what he / they did. After all, we had a lot in common, quite apart from our near parallel career tracks. We had no training whatsoever on the legal or regulatory ramifications of rate fixing. Furthermore, we were working as juniors for domineering bosses who brooked no disagreement, although Stelios and I probably coped better than Carlo.

There are two main reasons why I didn't make the same decisions. Firstly, we were doing jobs that were quite different. Rate fixing had a much bigger impact on the swaps book than on ours (to use some jargon, we were running much smaller delta positions), so seeking to influence fixing rates just doesn't seem to have been such a big part of the job.

And secondly, if you reread the accounts of my brush with rate fixing and Stelios' description, they are quite different. There is none of the furtive nature of Sergei's instructions when you read what Stelios writes. There is no reason for Stelios to suspect that anything fishy is going on. It's just presented as completely normalised behaviour.

I am still not completely sure why Sergei was so secretive, given the practice of adjusting fixes was so commonplace. Perhaps he had some prescience about whaat was going go happen in the future, perhaps it was for his own amusement as part of the 'test', or perhaps it was just his Russian upbringing. 



"Try to put yourself in my shoes and think about how you would have acted in my place"