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Summary of Hedge Fund Risk and Return Data
Risk Management and Hedge Funds
RISK IN HEDGE FUNDS
Risk is present in nearly every investment to differing degrees. Even defaultfree U.S. Treasury bills leave the investor with reinvestment risk. And risk (at least as it is often measured) is not inherently bad because it is usually associated with higher returns.
Nevertheless, it is important to measure risk, and that is the subject of this chapter. Chapter 7 shows ways to quantify the risk of the reported performance, using the standard deviation of return or volatility, downside deviations, the Sharpe ratio, the Sortino ratio, and other ex post measurements. In contrast, the methods presented in this chapter are forward-looking. Also, the measures in Chapter 7 rely only on the performance of the fund as a whole. This chapter presumes that the analyst has information about individual positions. In a time when investors frequently demand significant transparency, it is not unusual to have the details necessary for a robust risk analysis. Certainly, the funds have this position detail and often report results of risk analysis similar to those just described.
How Risky Is a Hedge Fund ?
Many people believe hedge funds are extremely risky. Certainly, the risk disclosure documents dont discourage this attitude. It is important to realize, though, that the risks described are designed to be the worst case, not the most likely case. Since hedge fund sponsors face much greater litigation risk from failing to disclose potential risks than from disclosing implausible risks, the documents sometimes make it difficult for investors to assess the likely risk of a hedge fund investment.
The media reports about hedge funds also dwell on the risks of hedge fund investing. Disasters make for good copy, so it is reasonable that bad news makes the front page and other hedge fund news appears inside, if at all. Further, in the 1990s, the large global macro hedge funds were newsmakers, and this is one of the riskiest hedge fund strategies. Unnoticed by the press (but not by hedge fund investors), many hedge funds came into existence offering modest returns and lower risks. The penchant for secrecy at many hedge funds may create a situation where the public never hears about the good news and only hears about the bad news when it is bad enough to become public information.
Sources of Hedge Fund Risk
Many factors contribute to the risk of hedge fund returns. The securities held by the fund, including stocks, bonds, currencies, commodities, and derivatives, contribute substantially to the risk of the portfolio. Hedge funds may choose to apply various hedging techniques to reduce the risk. The presence of leverage may amplify these security risks and introduce other risks. World central bankers are concerned that one of the risks of hedge funds is the collective stress they place on the financial system. Finally, recent history has demonstrated that at least sometimes, hedges fund fail because of outright fraud.
Summary of Hedge Fund Risk and Return Data
Figure 11.1 shows a plot of the risk and return of several hedge fund strategies from 1998 through January 2004. The hedge fund strategies are a collection of passive hedge fund indexes maintained by the Center for International Securities and Derivatives Markets (CISDM). That is, the passive indexes are built from a group of hedge funds actually open for new investment. The return of each group of funds is associated with a dozen or so economic factors (including stock returns, bond returns, credit spreads, market volatilities, etc.). Then, a performance is calculated from these economic variables for each passive strategy. The result is a representative benchmark of performance that is reasonably free from human errors, fraud, or other factors that are not representative of the hedge fund universe. These series do not benefit from diversification found in hedge fund indexes of many funds (sometimes called active indexes) so should be more representative of hedge fund returns than active indexes.
During this time period, stocks earned less than the long-term expected return of 10 or 11 percent that has been typical. As a result, hedge funds as a group outperformed the Standard & Poors 500 index and many other equity benchmarks. The relative performance of hedge funds versus the stock and bond indexes shown may not be representative in the future. When stock performance is good, it is typically higher than hedge fund returns, but the advantage of stock returns over hedge fund returns is determined mostly by how well the more volatile stocks perform.
The relative risk of hedge funds and stock and bond returns is more consistent. All the hedge fund strategies were less risky than the S&P 500 and about half were less risky than the more staid Lehman bond index representing a well-diversified bond portfolio. Perhaps hedge fund returns are less volatile than the securities the hedge funds trade because investors have been quick to pull money out of excessively risky hedge funds.
Table 11.1 shows a variety of risk measurements on the same passive hedge fund indexes. On every measure of risk, all strategies except the short selling index are less risky than the S&P 500.
Hedge funds control the risk of their positions using risk management techniques. The same tools can be used by investors, creditors, and regulators to monitor the risks in a hedge fund, provided that the fund discloses either details about portfolio holdings or the results of its internal risk analyzes.
FIXED INCOME RISK MANAGEMENT
The fixed income markets developed risk management tools earlier than commodity and equity markets because the largest source of risk for most fixed income instruments is interest rates, and interest rates (even for different bonds) move together more closely than either commodity prices or stock prices. Many of the fixed income risk management tools in use today derive from the work attributable to an insurance actuary developed more than a century ago.
Bond Pricing for a Regular Coupon Bond
The mathematics of fixed income risk management begins with fixed income valuation. The price of a bond with annual payments yielding r the formula provides the present value of the coupon payments. The form of price commonly used by market participants is the value called the net price (or full price minus the value of accrued interest).
This can be generalized for bonds paying interest monthly or semiannually. This shows the value of a bond paying semiannual coupon payments for 10 years.
Duration as a Measure of Bond Risk
The risk measure in equation (11.3) is called Macaulay duration. For simplicity, this formula is given for the case of a bond with a coupon paid annually.
Notice, however, that the interval of time from the settlement date (now) until each payment is included in the numerator. The denominator is a present value factor, and the remaining term is the particular cash flow. For this reason, duration is sometimes described as the present value weighted time to maturity of the cash flows.
The convenient feature of this modified duration is that it equals the percent change in price (in particular, the dirty price) caused by a change in yield of 1 percent (or 100 basis points). For example, a bond with a coupon of 5.5 percent and duration of 5 will decline from 100 to approximately 95 if rates rise from 5.5 percent to 6.5 percent.
Bond moves from 100 at 5.5 percent to 104.433 at 4.5 percent, slightly higher than predicted by modified duration, and to 95.789 at 6.5 percent, also slightly higher than predicted by modified duration. This imprecision results from convexity, described later.
A 10-year bond with a 5.5 percent coupon is more sensitive to changes in interest rates. The modified duration of this bond is 7.413. Figure 11.3 shows the price and yield relationships of this bond.
The price at 4.5 percent is 107.983, slightly higher than the price predicted by modified duration, and at 6.5 percent is 92.729, again slightly higher than the price predicted by modified duration. Further, notice that the modified duration of the two bonds correctly predicts that the 10-year bond will be considerably more sensitive to changes in interest rates.
Using Duration to Establish Trade Weightings
A hedge fund may use duration to establish a long position in one bond and short position in another bond so that the combination is hedged from changes in rates. For a particular change in rates equal to ?r, the gain or loss on the long position is the change in rate times the modified duration times the value of the full position. Equation (11.5) permits the trader to the dirty price as a percent of face value times the face value is the market value of the position. The modified duration is the percent change in market value for a 1 percent change in yield, and the change in yield scales the gain or loss to the amount of rate change. Each side of the equation represents a dollar amount.
The change in yield appears to be the same on both sides of the equation. If the yields of one bond are more volatile than the other, it is appropriate to include different values for the change in yields. Yields on shorter maturities tend to move more than yields on longer maturities. Yields on bonds with lower ratings may be more volatile than yields on bonds with higher ratings. The change in yields was presumed to be the same on both sides (called a parallel yield shift) so the term drops out
Duration as a Risk Management Tool
Knowing the duration of a bond allows the hedge fund manager to gauge the impact of changing interest rates on individual bonds. Fortunately, it is easy to extrapolate to the impact on a portfolio.
A portfolio with a duration of 5 will gain or lose about 5 percent of value for a change in yield of 1 percent or 100 basis points.
Using Short Positions in Bonds to Control Risk
Hedge funds are not restricted to long-only positions. By carrying long and short positions, hedge funds can set the portfolio duration at any level desired. This doesnt mean that the hedge fund has no risks. However, it is possible to estimate the gains or losses if the yields move the same amount on all bonds in the portfolio.
Convexity and Bond Prices
In the previous example, the price will not rise or fall exactly by the amount predicted by duration because the duration does not remain fixed at the original level. Notice that the yield to maturity (r) appears in equation (11.4). This means that as the bond price moves down from 100, the yield rises and the duration changes. When prices fall (rates rise), the modified duration declines, so the decline in price is smaller than the original forecast over this range of yields. Similarly, when prices rise (rates fall), the modified duration increases, so the rise in price is larger than the original forecast over this range of yields.
Because the y-axis is expanded to accommodate the even greater price sensitivity of a 30-year bond. Notice, too, that the modified duration of a 30-year bond varies. At higher yields, the price is less sensitive to changes in rate (flatter slope), and at lower yields the price is more sensitive to changes in rate (steeper slope). At 5.5 percent, this bond has a modified duration of 14.223. At 4.5 percent, the bond has a modified duration of 15.363, while at 6.5 percent, the modified duration is only 13.128.
Convexity measures the degree that durations change in response to changes in yield. The traditional formula for convexity is given for a bond with an annual coupon:
Convexity Is a Good Thing
In the example, the bond rose more than predicted by modified duration, a good feature for anyone who owns the bond. Also, the price declined less than predicted by modified duration, also a good feature for anyone who owns a bond. Bonds that have convexity benefit from this price behavior.
Some bonds have what is described as negative convexity: Prices rise less than predicted by duration when rates decline but fall further when rates rise. Some types of mortgage-backed bonds have this trait because of the prepayment option owned by the homeowner. Callable bonds may also exhibit negative convexity.
Using Duration and Convexity for Risk Management
It is possible to use duration and convexity to develop scenarios. These scenarios can highlight the risks in a hedge fund portfolio. However, it is simple enough to revalue the positions at different yields without relying on duration and convexity for approximations. The real value of duration and convexity totals on a portfolio is that they provide a very simple indication of interest rate exposure. Because of the simplicity of the two indicators, it is possible to create rules to hold the interest rate risk of the portfolio to a tolerable level.
CURRENCY RISK MANAGEMENT
A simple means to manage currency exposure is to reduce the complexity of currency exposures. At the risk of ignoring real currency risk, some traders have consolidated positions into two or three currencies. For example, Canadian dollar exposure is converted to U.S. dollar and any risk on the exchange relationship between Canada and the United States is ignored. Other currency exposures may be reduced to exposure to the euro and the Japanese yen.
This technique is called proxy hedging and is successful only if the actual currency exposures resemble the proxy currencies. In some cases, where a portfolio has exposure to many currencies, diversification may improve the results but cant guarantee success.
EQUITY RISK MANAGEMENT
Stocks face an even greater risk management problem than currencies. The correlation between most stocks is significantly lower than the correlation of bond returns. It is possible to apply proxy hedging in a way similar to the currency solution but the results are more unpredictable. Under this scheme, stocks are assigned to an index (S&P 500, Nasdaq, or a non-U.S. index, for example).
Ironically, the inability to completely track the indexes is ignored. Generally, these efforts start with the capital asset pricing model that hold that the return on a particular stock (ri) is driven by the return on a risk-free as set (rRiskFree), the return on the market (rMarket), and the amount of market risk present in the security (called beta and shown as Bi). See Equation (11.11). Risks particular to an individual stock are called nonsystematic risk and are assumed to vanish through diversification.
Stocks with betas of 1 are as risky as the market and are included without adjustment. Stocks with betas below 1 are underweighted in determining equity exposure, while stocks with betas above 1 are overweighted.
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