Managing Investor Drawdowns Through a Risk Control Plan: A New Model for Evaluating Manager Performance

By Tushar Chande
President
LongView Capital Management, L.L.C.

The three unknowns regarding the future performance of any money manager or trading system include:

• expected returns,
• depth of drawdowns, and
• duration of drawdowns.

Reasonable estimates for these three unknowns are required in order to invest confidently with a particular manager or trading system. These estimates also provide the basis of a Risk Control Plan, which can be invaluable in developing the confidence necessary for investors to remain with a manager through drawdown periods.

Creation of a Risk Control Plan involves defining a benchmark for returns, and developing estimates for expected returns, estimate depth of drawdowns, and duration of drawdowns. This information is then plotted in three dimensions, in a 'box' graphical representation, or Chande Comfort Zone (CCZ). This tool can then be used to monitor manager performance and to address whether a trading system has "stopped working."

A Benchmark For Long-term Returns

This inquiry begins by defining a benchmark for long term returns using the monthly Sharpe Ratio with the risk free rate set to zero. This is called the return efficiency (r) because it measures the return generated by the manager per unit of risk accepted by the investor.

                                                 Average Monthly Returns (m)

            Return Efficiency (r) =  ___________________________      (1)

                                      Standard Deviation of Monthly Returns (s_M)

Note that the ratio r=m/s has been identified by various terms in the literature, including information ratio and modified Sharpe Ratio. We prefer the term "return efficiency," analogous to the m.p.g. or miles-per-gallon for a car, because it measures how effectively a manager (the engine of the return generation process) converts the fuel (risk borne by the investor) into returns for the investor. A study of the long-term returns for commodity trading advisors (CTAs), hedge fund managers and stocks suggests that a good benchmark value for return efficiency is 0.25 (see Tables 1 and 2 below). This is also close to the value obtained by a simulation of a channel breakout system on a diversified portfolio.

In summary, the benchmark value for return efficiency is:

r_BM = 0.25.                                                   (2)

Notice that Tables 1 and 2 suggest that it is relatively difficult to exceed the benchmark over the long-term, and a manager exceeding this benchmark is adding significant value.

Estimating Expected Annual Return

Expected return is estimated by compounding the average monthly return (m) as follows:

R_E
= 100*((1+.01m)¹²-1) (%)
(3)

For example, if the average monthly return is 1 percent, then the annual expected return is approximately 12.7 percent. This equation, though well known, becomes more interesting when we substitute for the expected value of average monthly return, m from equations (1) and (2) above as follows:

R_E
= 100*((1+.01 r_BM s_M)¹²
-1) (%)  

R_E = 100*((1+.00025 s_M) ¹² -1) (%)                               (5)

Now we can substitute for the average monthly return into equation (3) to get:

Equation (5) is valuable because it demonstrates the direct connection between the volatility of a manager and the expected returns via return efficiency. These equations indicate that in order to obtain higher returns, an investor must bear greater risk (higher s) or find a more efficient manager (high r). For example, if a manager has a monthly standard deviation of 5 percent, one should reasonably expect annual returns of approximately 16 percent.

Estimating Depth of Drawdowns

Our research into estimated drawdowns is based on an analysis of monthly returns of CTAs, hedge funds, stocks and mutual funds. Hence, when we refer to peak-to-valley-drawdowns (PVDD or D), we are measuring drawdowns on a month-end basis. This typically is how the official values are calculated for reporting purposes. Our research into the PVDD reported by 110 CTAs is shown in Figure 1. Notice how the worst PVDD increases as the s_M,increases. A linear regression through the origin had slope of 2.84 approximately. Thus, to a good approximation, the PVDD was 3s_M,, and usually less than 4 s_M,. We will be conservative and write the relationship as follows:

D = 4 s_M                                                                       (6)

Our research shows similar curves for hedge funds and even mutual funds. This is a significant observation with important implications for risk control, because for CTAs and hedge funds the leverage can be adjusted to match the drawdown preferences of the investor.

Figure 1 : Worst Drawdown

The Connection between "Worst" Drawdown and Expected Returns

Since we know how to relate the PVDD to the volatility of a manager, we can work backwards and integrate this value into the expected return equation. The return efficiency of the manager converts the "worst" drawdown desired by an investor into potential future returns for that investor. To further clarify this idea, we substitute for  s_M from equation (6)

            R_E
= 100*((1+.01 m)¹² -1) (%)

            R_E
= 100*((1+.01 r s_M)¹²
-1) (%)

            R_E
= 100*((1+.01 r D/4)¹² -1)
(%)     

            R_E
= 100*((1+.0000625D) ¹² -1)
(%)                       (7)

Equation (7) shows the direct relationship between the worst drawdown an investor is willing to live with (D), or their threshold of pain, and the expected return. Hence, if the investor is willing to accept a 20 percent drawdown, and the manager had a return efficiency of 0.25, then the investor can expect a return of approximately 16 percent. Once again, to obtain higher returns, an investor must accept greater risk (higher D), or find a manager with a higher return efficiency (r). In short, there is no free lunch.

Estimating the Duration of Drawdowns

There are two approaches one can use to estimate the duration of drawdowns. We start by identifying the lengths of every drawdown period or "string" in the track record of the manager or trading program. These data can then be fitted to an exponential distribution, or we can calculate s_dd, the standard deviation of the lengths of drawdown strings (in months). Our analysis shows that to a good approximation, t, the duration of the longest drawdown can be expressed as follows (see Figure 2):

            t = 4s_dd                                                  (8).

Figure 2 : Duration of hedge fund drawdown

Chande Comfort Zone

We now have the tools to estimate the three key unknowns about future system performance: expected returns, and the depth and duration of drawdowns. Our methodology estimates the "upper-bound" of values that we can reasonably expect; therefore, they do not predict the actual values that will be realized in the future. We can plot these three quantities using a 3-dimensional grid to define a "box" or Comfort Zone within which one can reasonably expect a manager's performance to fall. Note that it is possible to realize results outside this box under particularly favorable or unfavorable conditions.

Figure 3 shows the general shape of the box, and its value lies in allowing managers and investors to decide if they are comfortable with the proposed dimensions of the box. If they are in agreement, managers should be able to maintain a long-term investment strategy without actively seeking modifications. If, at any time, managers or investors are not happy with the parameters of the box, it can be reshaped to meet the revised expectations.

Figure 3 : The Chande Comfort Zone

For example, let us assume that the projected drawdown for a particular strategy is 30%, but the manager wants to limit the high probability zone to 20%. This can be accomplished by reducing the leverage used in the strategy, or increasing the capital allocated to the strategy. Consider another scenario in which the duration of the drawdown is forecast to be 12 months, but the manager prefers it to be 7 months. In this case, there is a portfolio problem; the manager might combine the investment process under review with other return generation processes to reduce the duration drawdowns.

Most importantly the CCZ can be used to answer another important question: Has the system stopped working? This is a particularly difficult question since drawdowns are to be expected. However, the shape of the CCZ provides an answer. If the depth and duration of drawdown both lie outside the projected CCZ, then a detailed review of the return generation process is called for, since the system may have "stopped" working. Thus, the depth and duration of drawdown provide valuable benchmarks for assessing performance.

Let us assume that the CCZ projects a 22% drawdown lasting less than 12 months. If a manager experiences a drawdown of 25% lasting 13 months, then this is cause for concern and a review is probably necessary. However, it does not automatically mean that the system has "stopped working." In this example, a manager should assess if other traders with a similar strategy are also experiencing drawdowns, and also check for execution errors that may have led to losses. For example, a manager may increase the leverage used in trading in a bid to recover from a drawdown. Any significant deviation from the planned leverage level is certainly sufficient reason for review and reassessment.

The CCZ also provides valuable clues when the performance has been significantly better than expected. For example, when the CCZ projects a 25% return, but you are actually up 40%, it is worth checking the performance of managers with similar strategies, and looking for unusual deviations in execution, such as increased leverage or changes in the portfolio that may explain the performance.

The CCZ also provides clues related to when to add money to a trading manager, portfolio or return generation process. Let's say that the expected duration of drawdown is 8 months, and the manager is 5 months into the drawdown, and also assume that the expected severity of the drawdown is 20%, and the manager is down 10 percent. This may be a good opportunity to add some assets to this manager since the entry point is significantly below recent equity highs and the drawdown may be close to ending - assuming the exponential distribution parameters are stable. Additional due-diligence would also be necessary, to check if the manager has altered the strategy or reduced leverage.

The CCZ thus performs a useful function by defining the "expected" performance envelope, allowing the investor or allocator to take calculated risks while managing their investments.

Estimating a Risk Control Plan

The model for manager performance can be used to develop a Risk Control Plan (see Table 3). This process starts by establishing the risk-preferences of the investor, and uses the model to develop estimates for risk and return. The volatility estimates can be used to monitor the program performance in real-time. This plan is specific, objective, and derived from an existing track record. It can thus be a powerful tool for the manager and investor alike.

Table 3 : Sample Risk Control Plan Shows Risk/Return Tradeoffs

Summary

These new quantitative tools can be used to benchmark manager performance, and to derive clear risk-control guidelines, while managing investor expectations. They have been tested on data from CTAs, hedge funds, stocks and mutual funds, and thus can be applied to a broad range of asset classes.

Most importantly, these tools provide a strong basis for positive ongoing communication with investors, and allow investment professionals to establish and manage client expectations; thereby increasing adherence to a long-term trading strategy, and reducing the depth and duration of investor drawdowns.

References

Chande: "Estimating the Depth and Duration of Future Drawdowns from Past Performance Data", Managed Funds Association Newsletter, September, 1998.

Chande: "Controlling Risk and Managing Investor Expectations by Modeling the Dynamics of Losses in Hedge Funds and Alternate Investment Strategies", Derivatives Quarterly, Spring 1999.

Chande: "Beyond Technical Analysis", 2nd edition, to be published by John Wiley and Sons in June, 2001.

About the Author:

Tushar Chande is the president of LongView Capital Management, L.L.C., and has 10 years experience as a trader and CTA. He has a Ph.D. in Engineering and is the author of "The New Technical Trader" and "Beyond Technical Analysis", both from John Wiley & Sons. He can be reached at (515) 224-9100 or by e-mail at uptrend@attglobal.net.