CHAPTER 9 CHAPTER 9 Measuring the Long Volatility Strategies of Managed Futures Mark Anson and Ho Ho Certain hedge fund strategies create investment positions that resemble a long put op
Trang 1CHAPTER 9 CHAPTER 9 Measuring the Long Volatility Strategies of Managed Futures
Mark Anson and Ho Ho
Certain hedge fund strategies create investment positions that resemble a long put option Specifically, managed futures or commodity trading advisors have significant exposure to volatility events This exposure is pos-itively related to volatility much like a long option position We identify and measure this long volatility exposure, which may not always be transparent from the trading positions of a commodity trading advisor We also examine ways to apply these long volatility strategies to improve risk management
INTRODUCTION
The managed futures industry has come full circle in its application over the last 15 years In the early 1990s, global macro funds were the predominant form of the hedge fund industry These funds were primarily managed futures funds run by commodity trading advisors (CTAs) As the 1990s pro-gressed, other types of hedge fund strategies came to the forefront, such as relative value arbitrage, event driven, merger arbitrage, and equity long/short
As these strategies grew, managed futures became a smaller part of the hedge fund industry
Now, however, managed futures have achieved a renewed interest because of their risk reducing properties relative to other hedge fund strate-gies Specifically, most CTA strategies employ some form of trend-following strategy These trend-following strategies pursue both up- and down-market movements in futures markets These strategies also may be called momen-tum strategies because they follow the momenmomen-tum of the market and then liquidate their positions (or reverse them) when they detect that the momen-tum is changing or about to change
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Trang 2Whether we call managed futures trend-following or momentum stra-tegies, they have one important characteristic: They capitalize on the volatility
in the futures market Trend-following strategies tend to be “long-volatility” strategies; that is, they profit during volatile markets Long-volatility strate-gies can be useful risk management tools for other active trading stratestrate-gies that tend to be short volatility
We begin with a brief overview of the managed futures industry We then measure the long-volatility exposure captured these strategies Next
we apply Monte Carlo simulation to estimate the value at risk for long-volatility strategies Last, we demonstrate some practical risk management strategies that may be employed with managed futures
BRIEF REVIEW OF THE MANAGED FUTURES INDUSTRY
Managed futures is often referred to as an absolute return strategy because their return expectations are not driven by broad market indices, such as the Standard & Poor’s (S&P) 500, but instead by the specialized trading strategy of the commodity trading advisor More specifically, their return expectations are an absolute level of return sufficient to compensate them for the risk associated with trading in the futures markets This absolute level is established independently of the return on the stock market The managed futures industry is another skill-based style of investing similar to hedge fund managers In fact, managed futures is considered a subset of the hedge fund world Commodity trading advisors use their spe-cial knowledge and insight in buying and selling futures and forward con-tracts to extract a positive return This skill and insight can be applied regardless of whether the stock or bond markets are rising or falling, pro-viding the absolute return benefits described above
Commodity trading advisors have one goal in mind: to capitalize on price trends in futures markets Typically, CTAs look at various moving aver-ages of commodity prices and attempt to determine whether the price will continue to trend up or down, and then trade accordingly Some CTAs also use volatility models such GARCH (generalized auto-regressive conditional heteroskedasticity) to forecast both price trends and volatility changes Prior empirical studies have indicated that managed futures, or com-modity trading advisors, have investment strategies that tend to be long volatility Fung and Hsieh (1997a) found that trend-following styles have a return profile similar to a long option straddle position—a long volatility position Fung and Hsieh (1997b) documented that commodity trading advisors apply predominantly trend-following strategies
Trang 3In our research we use three Barclay Commodity Trading Advisor indices to capture the trading dynamics of the CTA market: Commodity Trading Index, Diversified Commodity Trading Advisor Index, and System-atic Trading Index These indices are an equally weighted average of a group
of CTAs who identify themselves as belonging to one of the three strategies There are alternative ways to gain exposure to the futures markets without the use of a CTA One way is a passive managed futures index, such as the Mount Lucas Management Index (MLMI)
The MLMI applies a mechanical trading rule for following the price trends in several futures markets It uses a 12-month look-back window to calculate the moving average unit asset value for each futures market in which it invests Once a month, on the day prior to the last trading day of the month, the algorithm examines the current unit asset value in each futures market compared to the average value for the prior 12-month period If the current unit asset value is above the 12-month average, the MLMI purchases the futures contract If the current unit asset value is below the 12-month moving average, the MLMI takes a short position in the futures contract
The MLMI invests in and is equally weighted across 25 futures con-tracts in seven major commodity futures categories: grains, livestock, energy, metals, food and fiber, financials, and currencies The purpose of its construction is to capture the pricing trend of each commodity futures con-tract without regard to its production value or trading volume in the market Our next step is to document the long volatility strategy of the man-aged futures industry
DEMONSTRATION OF A LONG VOLATILITY STRATEGY
In this section we use the direction of the stock market to demonstrate the asymmetric payout associated with managed futures That is, we expect that large downward movements in the stock market will result in large gains from managed futures Conversely, we expect that large positive movements in the stock market will result in a constant return to managed futures This type of return pattern is consistent with a long put option exposure Therefore, this section plots the direction of the stock market ver-sus the returns earned by managed futures In the “Mimicking Portfolios” section we specifically incorporate a measure of volatility to determine its impact on these hedge fund strategies
We start by producing a scatter plot of the excess return to the Barclay Commodity Trading Index returns versus the excess returns to the Standard
Trang 4& Poor’s (S&P) 100.1 We use the S&P 100 because this is the underlying index for which the VIX volatility index is calculated We use the VIX index
in the next section Figure 9.1 presents this scatter plot
On the scatter plot in Figure 9.1, we overlay a regression line of the excess return to the Barclay Commodity Trading Index on the excess return to the S&P 100 Note that the fitted regression line is “kinked.” The kink indicates that there are really two different relationships between the excess returns to the stock market and the excess returns to managed futures
To the right of the kink, the relationship between the returns earned by the CTAs and the stock market appears orthogonal That is, there is no apparent relationship between the returns to CTAs who pursue a diversified trading program and the returns to the stock market, when the returns to the stock market are positive
When the stock market earns positive returns, the Commodity Trading Index earns a consistent return regardless of how positive the stock market
–8.00%
–6.00%
–4.00%
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0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
–20.00% –15.00% –10.00% –5.00% 0.00% 5.00% 10.00% 15.00%
S&P 100 Excess Returns
CTA Regression Line
FIGURE 9.1 Barclay Commodity Trading Index
1 Excess return is simply the total return minus the current risk-free rate.
Trang 5performs This part of the graphed line is flat, indicating a constant, con-sistent return to managed futures when the stock market earns positive returns In this part of the graph, the excess return provided by the Com-modity Trading Index is almost zero That is, after taking into account the opportunity cost of capital (investing cash in treasury bills), the return to this style of managed futures is effectively zero, when there is no volatility event This result highlights a point about the managed futures industry: It
is a zero-sum game, similar to Newton’s law of physics: For every action, there is an equal and opposite reaction
However, to the left side of the kink, there is a distinct linear relation-ship between the returns to managed futures and the S&P 100 Declines in the stock market driven by volatility events result in large, positive returns for the Barclay Commodity Trading Index In fact, the fitted regression line
in Figure 9.1 mirrors the payoff function for a long put option
Figures 9.2 through 9.4 demonstrate a similar “kinked” relationship for the Barclay Diversified Trading Index, Systematic Trading Index, and the MLMI Each figure demonstrates a long put optionlike exposure In the next section, we examine how this kinked relationship can be quantified
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–20.00% –15.00% –10.00% –5.00% 0.00% 5.00% 10.00% 15.00%
S&P 100 Excess Returns
Diversified Trading Regression Line
FIGURE 9.2 Barclay Diversified Trading Index
Trang 6188 RISK AND MANAGED FUTURES INVESTING
–0.100 –0.050 0.000 0.050 0.100 0.150 0.200
–0.175 –0.150 –0.125 –0.100 –0.075 –0.050 –0.025 0.000 0.025 0.050 0.075 0.100 0.125
S&P 100 Excess Returns
Systematic Trading Regression Line
FIGURE 9.3 Barclay Systematic Trading Index
–0.080
–0.060
–0.040
–0.020
0.000
0.020
0.040
0.060
–0.175 –0.150 –0.125 –0.100 –0.075 –0.050 –0.025 0.000 0.025 0.050 0.075 0.100 0.125
S&P 100 Excess Returns
MLM Index Regression Line
FIGURE 9.4 MLM Index
Trang 7FITTING THE REGRESSION LINE
The previous discussion provides a general framework in which to describe empirically the long volatility exposure embedded within CTA trend-following strategies To fit the kinked regression demonstrated in Figures 9.1 through 9.4, we use a piecewise linear capital asset pricing model (CAPM)–type model The model can be described as:
where
In essence we plot two regression lines that have different alpha and beta coefficients depending on which side of the kink the market returns fall The trick is to maintain continuity at the kink in the fitted regression line To insure this, we impose this following condition:
Our regression equation then becomes:
We express our regression equation in this fashion to demonstrate how the threshold value is explicitly incorporated into the solution Table 9.1 pres-ents the results for our fitted regression lines
For the Barclay Commodity Trading Index, the threshold value (the
residual sum of squares in equation 9.3.
Trang 8TABLE 9.1
Regression R
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Trang 9coefficients First, the value of blowis negative and significant at the 5
returns to the S&P 100 are negative, the commodity trading strategies earn
that CTAs earn, on average, about a 0.4 percent excess return for every 1 percent decline in the S&P 100 below the threshold value
This is similar to a put option being exercised by the CTA manager when the returns to the stock market are negative, but created synthetically
as a consequence of the trend-following strategy As long as stock market returns remain positive, CTAs earn a constant return equal to a cash (treas-ury bill) rate However, when the stock market suffers a negative volatility event that drives market returns into negative territory, the synthetic put option is exercised, leading to large positive returns
returns when the returns to the stock market are positive When the returns
to the S&P 100 are positive, there is no need to exercise the put option In
this part of the graph Managed futures earn a treasury bill rate of return when the returns to the stock market are positive The lack of any excess return over this part of the graph can be considered the payment for the put option premium That is, trend-following CTAs forgo excess returns when the returns to the stock market are positive in return for a long put option exposure to be exercised when the returns to the stock market are negative Similar results are presented in Table 9.1 for diversified trading man-aged futures, systematic trading, and the passive MLMI index In each case,
has a negative sign, indicating positive returns to managed futures when the
cat-egory of managed futures Once again, this indicates that managed futures
do not generate any excess returns when the returns to the stock market are positive All that is received is a cash return equal to treasury bills
slop-ing curve However, the coefficient is small and lacks economic significance Still, this indicates that managed futures can be countercyclical when the stock market has positive returns
the other regression coefficients (see equation 9.2).
Trang 10MIMICKING PORTFOLIO
Here we specifically incorporate the long volatility exposure trend-following strategies to build mimicking portfolios of the strategies The idea is that if
we can build portfolios of securities that mimic the returns to CTAs, we can then simulate how trend-following strategies should perform under various market conditions
We use three components to build the mimicking portfolios: long OEX (options ticker symbol for S&P 100) put options, long the S&P 100 index, and long the one-month risk-free treasury security The long OEX put option
is used to capture the synthetic long put option exposure The long S&P 100 index is used to capture any residual market risk that exists when the mar-ket performs positively Last, we use the risk-free rate to measure the option premium that must be paid by CTAs to the right-hand side of the threshold value (when the stock market performs positively) We use the coefficient estimates from equation 9.3 to construct the mimicking portfolio
Long OEX Put Option
Volatility = VIX index
Long Risk-Free Security
Figures 9.5 through 9.8 present the results from our mimicking portfo-lios Similar to Figure 9.1, Figure 9.5 contains the scatter plot of the excess returns earned by the Barclay Commodity Trading Index plotted against the excess returns of the S&P 100 In addition, it contains the return of our mimicking portfolio
a long position in the stock market.