Proprietary trading: truth and fiction

may be available within an investment bank (we calculate our results assuming we pay commissions and Lnancing spreads). And of course, although we are housed in an investment bank, we have no access to any information about our bank 9s clients.<br><br> But there is always the possibility that we are exposed to risk factors that we don 9t know about. Managing risk We manage risk in two ways. First, for each strategy, we impose limits on some or all of the following: capital usage, expected portfolio standard deviation, value-at-risk (VaR), position liquid- ity, and exposure to various pre-identiLed risk factors (for exam- ple, a rho limit caps the Lrst derivative of portfolio return with respect to a parallel shift in interest rates).<br><br> Incidentally, our client, the bank, imposes overall limits on us for many of these variables and for some of their own. But the most important risk is the possibility of our models not working correctly. To minimize that risk, we set loss targets for strategies 4if we lose more money than the pre-speciLed target then the strategy is re-evaluated and shut down for a while (per- haps forever).<br><br> This is not that different from the old school of pro- prietary trader management: 8Go ahead and trade, don 9t do anything too risky, and if you lose more than $ x we 9re going to shut you down. 9 Our strategies are evaluated by looking at reward/risk mea- sures. For symmetric, market-neutral strategies without signiL- cant tail events, the Sharpe Ratio (SR) is probably the best ex ante measure. SR is deLned as the portfolio annual excess return divided by the annualized standard deviation of that return.<br><br> Our benchmark is cash, hence measuring excess returns is appropriate for our portfolio. For long-only managers, the Information Ratio 4which measures excess returns relative to a benchmark 4 is more appropriate. When we evaluate past performance, we also look at peak-to- trough drawdowns (a measure of the maximum drop between con- secutive maximum and minimum values of return over the life of the strategy) as an additional risk variable.<br><br> This can help pick up serial correlation in portfolio returns that the Sharpe Ratio doesn 9t capture. Also of interest is the fraction of expected gross proLts consumed by expected transaction costs. The higher this number, the more money we expect to lose if our model stops working.<br><br> At least some of our edge comes from opportunities that are created in the market by institutional managers who trade too much. Their trading is usually based on either an exaggerated view of how well they can predict investment returns, or a misun- derstanding of how trading costs increase with size. The strategies of institutional managers can still be perfectly rational despite providing us with opportunities through over-trading, simply because of the huge agency issues in portfolio management.<br><br> Incentives versus performance Investment strategies have Lxed capacities. As I increase the money invested in a strategy, my expected transaction costs increase while my pre-transaction cost estimate of expected return stays constant. Figure 1 shows an example of this 4once my marginal expected return, net of transaction costs, crosses zero, increased investment in a strategy only loses money.<br><br> Unfortunately for most investors who have delegated Lduciary responsibility to investment managers, investor and investment manager incentives are not well aligned. Almost all investment managers are paid a percentage of the funds under management. In the case of mutual funds and most institutional portfolios, this means their primary incentive is managing more funds.<br><br> Perfor- mance does also help determine reward, but only because it helps to keep assets or bring in more. I 9m not saying that investment managers don 9t try hard to deliver superior returns, rather that economic incentives move many successful managers to the right side of Lgure 1. The prob- lem is compounded by the signiLcant errors involved in estimat- ing the shape of the graph: most managers grossly overestimate their ability to forecast asset returns.<br><br> It 9s hard to turn people down Proprietary trading: truth and *ction Peter Muller , who has spent eight years building what he describes as a 8reasonably successful proprietary trading group 9, introduces some of the issues behind his strategies 4without giving his game away. Q UANTITATIVE F INANCE O PINION: P ETER M ULLER 7 who want to invest money with you, while it 9s easy to believe that one is further left on the graph in Lgure 1 than is actually the case. (N.B.<br><br> As an asset management Lrm grows, expected return may initially increase as a function of assets under management because additional compensation can be paid to improve one 9s investment process.) Hedge fund managers are incentivized both by a percentage of the proLts they make and by how much money they have under management. They are therefore less susceptible to the aforemen- tioned agency issues, but not entirely free of them. Asset manage- ment Lrms usually only collect management fees and trade at 8 312 times earnings; hedge fund managers also collect management fees and can still fetch 2 33 times earnings if they sell their Lrm.<br><br> By contrast, proprietary traders typically only earn a percent- age of their trading proLts (as in our case). There is no reward for holding more assets than we need, since we are charged Lnancing for all positions. Assuming the bank has good risk management controls in place, incentives are well aligned.<br><br> Excellent risk man- agement is essential to avoid giving too much value to a trader 9s free option (think Barings). Another way of mitigating the value of the option that a pay-out structure presents to the proprietary trader or hedge fund manager is to hold back compensation as a reserve against possible future drawdowns. This further aligns incentives and removes some of the asset substitution problem.<br><br> A simple study is suggested: rank investment-manager cate- gories by the risk-adjusted return of all managers in that category. It would be surprising if the underlying economic incentives did not determine the relative investment performance for each cate- gory. Proprietary traders have the purest incentive and would do the best, hedge fund managers would come next and institutional portfolio managers last.<br><br> I believe this is the case even if you include the well-publicized disasters that have occurred over the years in hedge fund management and proprietary trading. Getting accurate data on proprietary trading performance is probably too difLcult to make such a study feasible, but the literature on hedge fund performance that tries to estimate the performance of the group as a whole is consistent with these assertions. (See 8Further reading 9below.) More simply: if your investment Lrm has a marketing depart- ment, you 9re probably not that good an investor.<br><br> See Lgure 2. Creating a high Sharpe Ratio strategy How does one go about creating a high Sharpe Ratio strategy? Well, you 9re not going to get much advice from me 4sorry!<br><br> I will, however, address two issues. First, should one try to build one really great strategy or put together a bunch of good strategies? Second, how do shorter and longer horizon strategies differ?<br><br> In Grinold and Kahn 9s book on Active Portfolio Management (see 8Further reading 9), the authors describe the 8Fundamental Law of Active Management 9: a strategy 9s Sharpe Ratio is propor- tional to the number of independent bets taken by the strategy multiplied by the correlation of those bets with their outcome (Lg- ure 3). To get a higher SR, you need to increase the number of your bets or increase the strength of your forecasts. In my opinion it is far better to reLne an individual strategy by increasing both the number of bets within the strategy and the strength of the forecasts made in the strategy, than to attempt to put together lots of weaker strategies.<br><br> Depth is more important than breadth for investment strategies. As a strategy develops, betting opportunities increase and returns for each bet increase. But a huge transaction-cost barrier must be overcome before a strategy becomes proLtable.<br><br> Once this is overcome, additional improvements will leverage proLt much more efLciently than initial research will. Even though these improvements are harder to come by, the work is worth the effort. I know a proprietary trader who was offered extra compensation by a smart investor if he focused solely on improving his original 60 50 40 30 20 10 0 310 320 330 340 Position size Net excess expected profits Marginal transaction cost Marginal expected return Cumulative value added Figure 1.<br><br> Investment level versus excess proLts earned. DAVIDLAXER O PINION: P ETER M ULLER Q UANTITATIVE F INANCE 8 strategy instead of developing a strategy in a different area. He ended up Lguring how to increase the returns to his original strat- egy many times over.<br><br> If trading costs are added to the equation in Lgure 3, the rela- tionship between forecast strength and Sharpe Ratio stops being linear and looks more like Lgure 4. (Interestingly, the experience of many of the proprietary traders and hedge funds managers I know looks just like that graph, only with 8effort 9on the x- axis and 8 reward 9on the y -axis.) I would much rather have a single strategy with an expected Sharpe Ratio of 2 than a strategy that has an expected Sharpe Ratio of 2.5 formed by putting together Lve supposedly uncorre- lated strategies each with an expected Sharpe Ratio of 1. In the lat- ter case you 9re faced with the risk that the strategies are more correlated than you realize (think Long Term Capital).<br><br> There is also the increased effort of ascertaining whether each individual strategy really has a Sharpe Ratio of 1. Of course, choosing where to dig is important. There are well- established model-driven groups doing convertible arbitrage, mortgage-backed arbitrage, futures trading, long 3short equity statistical arbitrage and option arbitrage.<br><br> Some use more than one of these strategies, but to make signiLcant reliable proLts in these areas, you need to put in enough work to become one of the best players in each one. Short versus long horizon strategies An important choice for many proprietary traders is whether to focus on shorter or longer horizon strategies. Typically, shorter horizon strategies get their edge from providing temporal liquidity to a market place or predicting short-term trends that arise from inefLcient trading.<br><br> Longer-term models focus on asset pricing inef- Lciencies. How does implementation of these strategies compare? Shorter-horizon investment strategies are desirable because they tend to create higher Sharpe ratios.<br><br> If your average holding period is a day or a month, you have the opportunity of placing many more bets than if you hold positions for three months to a year or longer. On the Mip side, shorter horizon strategies tend to have capacity issues (it 9s easy to make a small amount of money with them, harder to make a lot of money). Shorter horizon strate- gies also require serious investments in trading infrastructure, since quick and inexpensive execution is much more important than for longer horizon strategies.<br><br> Risk management for shorter horizon strategies tends to occur through position trading rather than portfolio construction. Assets are not held for long periods of time and portfolio characteristics change quickly. The biggest risk for shorter horizon strategies is model risk, or the risk that the trading strategy deployed has stopped working.<br><br> Since even the best trading strategies experi- ence periodic drawdowns, the hardest challenge for the short-term model-based trader is to Lgure out whether his model is going through a regular drawdown or has stopped working altogether. Longer-horizon model-driven investment strategies have dif- ferent issues. Since assets are held for longer periods of time, exe- cution costs (although still important) are not the primary focus.<br><br> Statistical inference becomes more difLcult and the danger of overLtting or mining data becomes larger. Risk management for longer-term strategies happens in portfolio construction: since rebalancing occurs less frequently, more care needs to be taken to ensure the portfolio is not exposed to unintended sources of risk. Because they tend to have lower Sharpe ratios, longer horizon strategies have a different kind of capacity issue 4the manager 9s capacity for pain.<br><br> However, there is one advantage: because trad- ing occurs less frequently it 9s possible to lead a much better lifestyle than if you 9re running shorter horizon strategies! Conclusion My aim in this article was to be informative (and occasionally entertaining) while not telling you anything that my competitors or potential competitors would Lnd useful. Unfortunately, the mere knowledge that it is possible to beat the market consistently may increase competition and make our type of trading more dif- Lcult.<br><br> So why did I write this article? Well, one of the editors is a friend of mine and asked nicely. Plus, chances are you won 9t believe everything I 9m telling you.<br><br> And if you do, well, I 9ve always liked a challenge. Further reading Grinold RC and Kahn RN 1999 Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk (Probus) Goetzmann WN, Ibbotson RGand Brown SJ Offshore hedge funds: survival and performance 1989 31995 J. Business 72 91 3117 Why hedge funds make sense Global Equity and Derivative Markets (Morgan Stanley Dean Witter) November 2000 Peter Muller is Managing Director, Head of Process Driven Trading, at Morgan Stanley Dean Witter, New York.<br><br> Sharpe RatioMarketing department d 0Runs the Lrm 0.25Very important; involved in all investment decisions; major focus on asset gathering 0.5 31.0Secondary 1.0 32.0Almost superMuous e 2.0What marketing department? SR : Sharpe Ratio. N : Number of independent bets.<br><br> IC : Information coefLcient (correlation of bet with outcome). SR 2 N \x2 IC 2 1 3 IC 2 Information coefficient Sharpe Ratio Figure 4. Grinold and Kahn (1999) with transaction costs.<br><br> Figure 2. Investment Lrm politics. Figure 3.<br><br> The fundamental law of active management (Grinold and Kahn 1999).

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