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In preparation for resuming our exploration of hedge fund trading strategies, we took a detour last time out to learn about bond futures and conversion factors, which are used in basis trading.  Basis trading is a form of fixed-income arbitrage that seeks to benefit from a change in the spread between a spot bond price and an adjusted futures price.  The formula for the basis is:

B = SP – (FP x CF)

where:

B is basis

SP is spot price of bond (clean)

FP is futures contract price (clean)

CF is conversion factor

Clean prices are ones in which the present value of future cash flows, such as interest payments, are not included in the price.  Normally, one purchases a bond at the dirty price, which includes such cash flows.

A bond basis trade is the simultaneous purchase and sale of a bond and a bond futures contract to capture a non-zero basis as profit.  It is also known as a cash-and-carry trade.  (There is an alternative method of achieving the same result using exchange of futures for physicals (EFP) which we’ll not discuss in this article).

The conversion factor is the key to a basis trade.  Here’s how it works:

  • If the basis is negative, the bond spot price is less than the adjusted futures price. In this case, you would “buy the basis” by buying cash bonds and selling futures contracts. Say that the conversion factor on the 8 ¾ T-Bonds of 5/15/2017 is equal to 1.077. To buy $100M of the basis, you purchase $100M face value of the bonds and simultaneously sell 1,077 (= $100M * (1.077 / $100K) of bond futures.
  • If the basis is positive, the bond spot price is greater than the adjusted futures price. Here you would “sell the basis” by selling cash bonds and buying futures contracts.  For instance, if the conversion factor on the 7 5/8 T-Bonds of 2/15/2005 equals .0960, then selling $10M of the basis would require selling $10M face of the bonds and buying 96 futures contracts.

To close out the trade, you need to purchase your short position and sell your long position.  If you compare the opening spread with the closing one, the difference is the change in basis during the holding period.  A narrowing spread favors the short position; a widening spread benefits the long.

If you think the spreads will narrow over time, you benefit from selling the expensive bonds and buying the cheap futures contracts if your prediction is correct.  The change in basis over time is the cash part of the trade. The carry portion consists of coupon payments less financing costs (at the repo rate) for the bond (including accrued interest).  You realize a profit if the sum of the cash and carry portions are positive.

Every 1/32 of a basis point is worth $31.25; on a position of $10M face, this equals $3,125. Therefore, if a basis narrows by 2.6 basis points, the short position profits on the cash portion of the $10M face trade by 2.6 * $3,125 = $8,125. As long as the short’s carry costs do not exceed $8,125, he/she will pocket a profit.

The risk in a basis trade is that the basis will move in an unfriendly direction due to a change in the yield curve, and/or the repo rate will change to your disadvantage.  These changes are important because of the following reasons:

1)     If the repo rate decreases, or if the yield curve steepens, carry and basis increases

2)     A decrease in the bond’s yield relative to other deliverable bonds will increase the basis

3)     Bond duration can affect a bonds response to yield changes: the basis of a low-duration bond will tend to rise with bond yields, whereas the basis of a high-duration bond increases when bond yields fall.

4)     Volatility affects technical considerations involving the short’s strategic delivery options. A rise in volatility would tend to lower the futures price and raise bond basis.

There is extensive literature on basis trading, and interesting parties are urged to seek it out before embarking on any trading activity.

Our next topic will be asset swap trades.

Our review of hedge fund trading strategies continues with a discussion of yield-curve arbitrage (YCA), a form of fixed income arbitrage. I have previously written about the yield curve, convexity, and duration. Recall that for bonds not offering embedded features (such as puts and calls), a bond’s price and the interest yield move in contrary directions, giving an inverse association involving duration and yield. Higher yields mean shorter durations. The $duration of a bond is product of the duration and the price (value); with units of dollar-years, it reflects duration changes in dollars rather than in percentages.

A parallel shift in a yield curve occurs when the yield on all maturities change by the same amount. More likely are changes in which the spread between short and long maturities increase (steepen) or decrease (flatten).  A dumbbell portfolio is loaded up on bonds at the short and long ends of the yield curve; conversely, a bullet strategy involves the purchase of intermediate-maturity bonds.  Yield-curve arbitrage is a trading strategy in which a trader exploits relative mispricings along the yield curve due to high institutional demand for selected maturities, among other reasons.

A well-known form of YCA is the so-called butterfly trade: long dumbbells (the “wings” of the butterfly) and short bullets (the butterfly’s “body’) in a net-zero $duration spread trade.  For example, you might set up a portfolio in which you are long 4-year and 8-year maturities, and short 6-year maturities.  Small parallel moves in the yield curve would have little effect on this portfolio, since it has a net $duration of zero.  However, large parallel moves in either direction will guarantee a positive return due to the positive convexity (yield vs. price) of the portfolio – in effect, one expects greater convexity in the wings than in the body. That sounds good in theory; in practice, yield curves usually experience complex movement patterns that can have an unexpected affect on the outcome of a butterfly trade.

There are four popular types of butterfly trades:

  1. Cash and $duration neutral weighting – No cash is needed up front, since the cost of the long positions is offset by the proceeds from the short sale. Suitable prime brokerage structures are available such that the long position acts as collateral for the short position, so that zero cash flow is required initially. This strategy benefits from a flattening of the yield curve, because most of the $duration is in the wings of the butterfly.
  2. Fifty-fifty weighting regression – The trade is structured such that each wing of the butterfly has equal $duration. This strategy benefits from small changes to the yield curve, because the body is less convex than the wings. The position profits from a steepening of the yield curve. Note that this trade is not cash neutral, so return must exceed the cost of carry.
  3. Regression weighting – A sophisticated trade in which the linear regression measuring the spread between the short wing and the body is regressed against the spread between the body and the long wing.  The more-volatile short wing is more likely to move away from the body than is the long wing.  So, say for example we determine a regression coefficient of 0.5; it means that a 20 basis-point change in the short wing spread would imply a 10 basis-point move in the long wing spread. Since most of the $duration is in the long wing of the spread, the strategy benefits from a flattening of the yield curve.
  4. Maturity weighting – The relative maturities of the three components (short wing, body, and long wing) are used as the weighting of each component. The results of this strategy are very similar to the regression weighting scenario, except that the weighting factor will generally be higher than the regression coefficient.

There are calculated risk measures that can be used by traders to determine whether the spread on each of the butterfly strategies is attractive and invites investment.  Advanced readers can look up the model developed by Nelson and Siegel[1] to see how to partially hedge the risk exposures of different butterfly spreads.

Next time, we’ll continue our survey of fixed income arbitrage by taking a close look at basis trading.


[1] Nelson, C.R., and Siegel A.F., (1987) “Parsimonious Modeling of Yield Curves”, Journal of Business,

60 (4), , p.473-489.

Several months ago we began a conceptual review that will eventually lead us to evaluate hedge fund replication.  We have so far looked at various pricing models, described systematic (beta) and non-systematic (alpha) returns, and have started to explore different hedge fund trading strategies.  We continue today with short-selling strategies.

Shorting a stock means selling shares you do not own in the hopes of benefiting from a decline in the price of the shares.  The seller borrows shares, usually from a broker, and delivers them to a buyer in return for cash.  The cash proceeds are parked with the lending broker as collateral, where it earns short rebate interest for the seller. At some future point of time, the seller will need to return the borrowed shares to the broker by going out into the open market to purchase replacement shares.  Any price decline between the original sale and the subsequent purchase is profit for the seller. Conversely, if the shares appreciate over the interval the seller will register a loss. The capital gain or loss, plus the short rebate interest, minus any transaction costs (i.e. broker fees, stock-lending fees, exchange fees, etc.), represents the net P&L to the short seller.

In addition to holding the seller’s cash proceeds as collateral, most lending brokers require an additional pledge of cash or cash-equivalents (such as Treasury bills) in an amount ranging from 30% to 50% of the shares’ market value.  In the United States, SEC rules stipulate that short sellers must already have custody (either through ownership or borrowing) of shares sold.

Some managers execute short-selling strategies without the use of borrowed shares; rather, they utilize derivates to create downside exposure.  Forwards, futures, and options (on indices and stocks) are suitable derivatives for a short-selling strategy. The collateral requirements on derivatives are much less onerous, and provide short-sellers with additional leverage on their investments.  Other managers hedge their short sales with long positions that partially offset the short ones.  This creates a Long/Short strategy with a short bias.

One shorting technique, called shorting against the box, is not part of the hedged equity short selling strategy.  Rather, it involves offsetting all of a long position with a short sale in order to lock in a profit on shares that, for various reasons, an investor does not want to sell at the current time.

Long and short hedging strategies share a number of similarities, including careful stock picking and timing. Many practitioners of either strategy engage in bottoms-up fundamental analysis to identify mispriced stocks.  However, a short strategy fund manager is also likely to concentrate on certain negative factors, such as aggressive accounting techniques or revised quarterly earnings estimates. But it is not valid to think of a short selling strategy as simply the inverse of a long strategy – here are a few ways short selling has unique risks:

  • Stock-borrowing considerations: Short sellers need to locate shares to borrow, which for a hot stock may be expensive or unavailable.  They must be prepared for the lender to suddenly call back its shares, and they must negotiate a good short rebate rate.
  • Short squeezes: If a stock suddenly gains in price, a short seller may be forced to terminate his/her position prematurely by purchasing high-priced replacement shares, thus locking in a loss.
  • Performance/exposure:  Long strategies benefit from higher prices not only by higher market values but also because the winning shares now represent a larger portion of a portfolio, and thus increase relative exposure to a profitable stock. The situation is reversed for short sellers – loser stocks do engender a profit, but they lose portfolio share as the price declines, and hence decrease the short-sellers relative exposure to the shares.
  • Uptick rule: The U.S. recently reintroduced the uptick rule, which states that shares can only be shorted after an uptick.  In practice, hedge funds and other investors are usually able to manufacture an uptick when one is needed, but this is not foolproof.
  • Unlimited upside risk:  Stocks have a downside limit of zero but theoretically no upside limit. This creates an asymmetrical risk for short sellers that can have a negative psychological impact on the desire to short sell.

These factors, plus certain cultural and/or legal barriers to short selling, including a general reticence by investment analysts to issue “sell” recommendations, can tend to depress short selling activity.  Studies show that barriers to short selling artificially inflate stock prices.  Thus, short selling can be seen as an effective method to arbitrage “correct” prices in stock markets.

A pure short strategy, much like a pure long one, can benefit from investor skills.  What is not clear in either strategy is whether returns are consistently based on superior investor skill (alpha), on systematic exposure to one or more risk premia (beta), or a mixture of the two.

Next time we will start exploring relative-value trading strategies.

Non-diversifiable risk

We are reviewing the underlying assumptions made by the Capital Asset Pricing Model (CAPM).  Recall from last time the assumption that returns are distributed normally (i.e. a bell-shaped curve) and how this fails to account for skew and fat tails. Today we’ll look at CAPM’s assumption that there is but a single source of priced systematic risk: market beta.

Beta, of course, refers to the correlation between the returns on an asset and the returns on the broad market. Specifically, it is defined as:

βi  = Cov(Rm, Ri) / Var(Rm)  for asset i

that is, the covariance of the asset’s returns with the those of the market divided by the variance of the market returns.  Another way to think about beta is as a discount factor: when divided into an asset’s expected return, it adjusts the expected return so that it equals the market’s expected return.

By making this assumption, CAPM is able to simplify the universe of different risks undertaken by a portfolio, such as a hedge fund, to one global number. That’s good for ease of calculation but bad for reflecting reality. It is also assumed that all non-systematic risk (alpha) has been diversified away by having a sufficiently large portfolio, so that the expected return on the portfolio is a function of its beta alone.

Many academics challenge the use of variance in the formula for beta. They point out that variance is a symmetrical measure of risk, whereas investors are only concerned about loss (just the left side of the curve). Instead of variance, they point to other measures of risk, such as coherent risks, that may better reflect investor preferences.  Coherent risks have four attributes:

1)      When comparing two portfolios, the one with better values should have lower risk

2)      The joint risk of two portfolios cannot exceed the sum of their individual risks

3)      Increasing the size of positions within a portfolio increases its risk

4)      Picture two identical portfolios except one contains additional cash. The one with the extra cash is less risky, to the exact extent of the extra cash.

Hedge funds clearly take on risks that are not reflected in beta. These risks are the basis for the returns of many strategies, such as long/short (liquidity risk), fixed income (credit risk), and sector trading (sector risk) to name a few.  To the extent that a hedge fund takes on risks that are not reflected by beta, it is modifying its long-term expected return for better or worse.  For instance, a portfolio may add an asset with a negative expected return in order to hedge another asset that has an expected positive return. This has the effect of lowering the expected return of the portfolio as it lowers the portfolio’s risk.

Recall that the expected market return above the risk-free rate is called the market’s risk premium.  Many hedge funds seek returns independent of the market risk premium. Rather, hedge funds supposedly choose their risk exposures, and hence their risk premia. Ideally, their market beta would be zero, so that hedge fund returns would reflect only risks other than market risk. Note that these non-market risks are often hard to diversify away.  For instance, it is difficult to diversify away the risks involved in “risk arbitrage” – a misnomer for the strategy of taking positions on mergers and acquisitions. By assuming this “event risk” (i.e. by betting on whether a proposed merger will succeed), fund managers hope to capture the associated risk premium, independent of market beta.

There are a large number of hedge fund strategies, and most are exposed to their own systematic risks.  Later on, we will review different strategies in detail, and look at the associated risk premia at that time. The important point here is that systematic risk, whether captured in market beta or due to strategy-specific risk(s), should not be conflated with alpha – the returns due to superior skill and/or timing. Ultimately we will be exploring the case for and against alpha when we examine hedge fund replication strategies.

Next time, we’ll finish discussing the assumptions underlying CAPM.

Prime brokers offer a variety of services to investors, from providing credit to clearing trades. One important service offered is known as Securities Lending. In Part One of this article, we’ll look at the contractual and collateral rules pertaining to Securities Lending.

As an investor or hedge fund, you may wish to borrow shares for a variety of reasons, such as shorting the stock or hedging a long position. An executed Securities Lending Agreement is the documentation required before shares are loaned. Continue reading “Securties Lending, Part One” »

Our quest continues to find out whether hedge fund alpha really exists or is just hype. Recall from last time our documentation of the Capital Market Line (CML).  The CML represents a portfolio containing some mixture of the Market Portfolio (MP) and the risk-free rate. It is a special version of the Capital Asset Line, ranging from the risk-free rate tangentially to the Efficient Frontier at the Market Portfolio, and then extending upwards beyond the tangent point.  Modern Portfolio Theory (MPT) posits that any point on the CML has superior risk/return attributes over any point on the Efficient Frontier.  Let’s ponder that for a second – just adding some T-Bills to, say, S&P 500 baskets (our proxy for the Market Portfolio) will improve the risk/return characteristics of your portfolio.

Capital Market Line

If your entire portfolio consisted only of the cash-purchased Market Portfolio (i.e. the tangent point on the Efficient Frontier), your leverage ratio would be 1 – you are unleveraged. The points on the CML below the Market Portfolio represent deleveraging: adding cash to your portfolio.  You are lowering risk and expected return when you deleverage. If you borrowed and sold TBills, and used the proceeds to buy additional Market Portfolio, your new portfolio would be leveraged, and would be a point on the CML above the tangent. Leveraging increases your risk and expected return. If you disregard the effects of borrowing (or margin) costs, then all points on the CML share the maximum Sharpe Ratio, a popular formula for expressing risk/return. Continue reading “Modern Portfolio Theory – Part Three” »

Our risk/return series continues with a review of Modern Portfolio Theory (MPT). We’ve already looked at alpha, beta, efficient markets, and returns.  Our ultimate goal is to evaluate the role of alpha in hedge fund profitability, how to replicate hedge fund results without needing alpha, and finally how you can start your own cutting-edge hedge fund using beta-only replication techniques.

MPT suggests that a portfolio can be optimized in terms of risk and return by carefully mixing individual investments that have widely differing betas. Recall that beta is return due to correlation with an overall market (known as systematic risk). To take a trivial example, if you hold equal long and short positions in the S&P 500 index, your portfolio would have an overall beta of (.5 * 1 + .5 * -1) = 0.  There would be no risk, but in this case, there would be no return either, except for the slow drain of commissions, fees, etc.

Continue reading “Modern Portfolio Theory – Part One” »

If you have been following our recent blogs, you are by now familiar with the concepts of alpha, beta, and the Efficient Market Hypothesis.  Our final goal is to evaluate the role of alpha in hedge fund investing, and to look at trading strategies that do not rely on alpha.  Before we can discuss these topics, we need to better understand financial asset pricing models, the role of alpha and beta within these models, and how the models apply specifically to hedge funds. In this installment, we’ll review the concept of rate of return (ROR).

Continue reading “Rate of Return” »

In our previous blog, we discussed the concept of beta as it applies to the risk and return of an investment. Recall that beta is the price movement in an individual investment that can be accounted for by the price movement of the general market.  If your investment has a beta of 1.0 and the market returns 10%, your investment should also return 10%.  If your investment returns over 10%, the excess return is called alpha. Alpha is derived from a in the formula Ri = a + bRm which measures the return on a security (Ri) for a given return on the market (Rm) where b is beta.

Continue reading “Risk and Return: Alpha” »