Last Updated on Mon, 07 Jun 2021 | Hedge Funds

Hedge fund managers tend to use the term arbitrage somewhat loosely. Arbitrage is defined simply as riskless profits. It is the purchase of a security for cash at one price and the immediate resale for cash of the same security at a higher price. Alternatively, it may be defined as the simultaneous purchase of security A for cash at one price and the selling of identical security B for cash at a higher price. In both cases, the arbitrageur has no risk. There is no market risk because the holding of the securities is instantaneous. There is no basis risk because the securities are identical, and there is no credit risk because the transaction is conducted in cash.

Exhibit 3: HFRI Short Selling Index


1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000




1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000


Instead of riskless profits, in the hedge fund world, arbitrage is generally used to mean low-risk investments. Instead of the purchase and sale of identical instruments, there is the purchase and sale of similar instruments. Additionally, the securities may not be sold for cash, so there may be credit risk during the collection period. Last, the purchase and sale may not be instantaneous. The arbitrageur may need to hold onto his positions for a period of time, exposing him to market risk.

Convertible arbitrage funds build long positions of convertible bonds and then hedge the equity component of the bond by selling the underlying stock or options on that stock. Equity risk can be hedged by selling the appropriate ratio of stock underlying the convertible option. This hedge ratio is known as the delta and is designed to measure the sensitivity of the convertible bond value to movements in the underlying stock.

Convertible bonds that trade at a low premium to their conversion value tend to be more correlated with the movement of the underlying stock. These convertibles then trade more like stock than they do a bond. Consequently a high hedge ratio, or delta, is required to hedge the equity risk contained in the convertible bond. Convertible bonds that trade at a premium to their conversion value are highly valued for their bond-like protection. Therefore, a lower delta hedge ratio is necessary.

However, convertible bonds that trade at a high conversion value act more like fixed income securities and therefore have more interest rate exposure than those with more equity exposure. This risk must be managed by selling interest rate futures, interest rate swaps, or other bonds. Furthermore, it should be noted that the hedging ratios for equity and interest rate risk are not static, they change as the value of the underlying equity changes and as interest rates change. Therefore, the hedge fund manager must continually adjust his hedge ratios to ensure that the arbitrage remains intact.

If this all sounds complicated, it is, but that is how hedge fund managers make money. They use sophisticated option pricing models and interest rate models to keep track of the all of moving parts associated with convertible bonds. Hedge fund managers make arbitrage profits by identifying pricing discrepancies between the convertible bond and its component parts, and then continually monitoring these component parts for any change in their relationship.

Consider the following example. A hedge fund manager purchases 10 convertible bonds with a par value of $1,000, a coupon of 7.5%, and a market price of $900. The conversion ratio for the bonds is 20. The conversion ratio is based on the current price of the underlying stock, $45, and the current price of the convertible bond. The delta, or hedge ratio, for the bonds is 0.5. Therefore, to hedge the equity exposure in the convertible bond, the hedge fund manager must short the following shares of underlying stock:

10 bonds x 20 conversion ratio x 0.5 hedge ratio = 100 shares of stock.

To establish the arbitrage, the hedge fund manager purchases 10 convertible bonds and sells 100 shares of stock. With the equity exposure hedged, the con vertible bond is transformed into a traditional fixed income instrument with a 7.5% coupon.

Additionally, the hedge fund manager earns interest on the cash proceeds received from the short sale of stock. This is known as the short rebate. The cash proceeds remain with the hedge fund managers prime broker, but the hedge fund manager is entitled to the interest earned on the cash balance from the short sale (a rebate).10 We assume that the hedge fund manager receives a short rebate of 4.5%. Therefore, if the hedge fund manager holds the convertible arbitrage position for one year, he expects to earn interest not only from his long bond position, but also from his short stock position.

The catch to this arbitrage is that the price of the underlying stock may change as well as the price of the bond. Assume the price of the stock increases to $47 and the price of the convertible bond increases to $920. If the hedge fund manager does not adjust the hedge ratio during the holding period, the total return for this arbitrage will be:

Appreciation of bond price: Appreciation of stock price: Interest on bonds: Short rebate: Total:


If the hedge fund manager paid for the 10 bonds without using any leverage, the holding period return is:

However, suppose that the hedge fund manager purchased the convertible bonds with $4,500 of initial capital and $4,500 of borrowed money. We suppose that the hedge fund manager borrows the additional investment capital from his prime broker at a prime rate of 6%.

Our analysis of the total return is then:

Appreciation of bond price:

10 x($920 -

$900) =


Appreciation of stock price:



Interest on bonds:

10 x $1,000 x 7.5% =

= $750

Short rebate:

100 x $45 x <

4.5% =


Interest on borrowing:

6% x $4,500




And the total return on capital is: $682.5 - $4,500 = 15.17%

10 The short rebate is negotiated between the hedge fund manager and the prime broker. Typically, large, well-established hedge fund managers receive a larger short rebate.

Exhibit 4: HFRI Convertible Arbitrage Index


1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000


The amount of leverage used in convertible arbitrage will vary with the size of the long positions and the objectives of the portfolio. Yet, in the above example, we can see how using a conservative leverage ratio of 2:1 in the purchase of the convertible bonds added almost 500 basis points of return to the strategy. It is easy to see why hedge fund managers are tempted to use leverage. Hedge fund managers earn incentive fees on every additional basis point of return they earn. Further, even though leverage is a two-edged sword — it can magnify losses as well as gains — hedge fund managers bear no loss if the use of leverage turns against them. In other words, hedge fund manages have everything to gain by applying leverage, but nothing to lose.

Additionally, leverage is inherent in the shorting strategy because the underlying equity stock must be borrowed to be shorted. Convertible arbitrage leverage can range from two to six times the amount of invested capital. This may seem significant, but it is lower than other forms of arbitrage.

Convertible bonds are subject to credit risk. This is the risk that the bonds will default, be downgraded, or that credit spreads will widen. There is also call risk. Last, there is the risk that the underlying company will be acquired or will acquire another company (i.e., event risk), both of which can have a significant impact on the companys stock price and credit rating. These events are only magnified when leverage is applied.

Exhibit 4 plots the value of convertible arbitrage strategies versus the S&P 500. Convertible arbitrage earns a consistent return but does not outperform stocks in strong bull equity markets.

Continue reading here: Fixed Income Arbitrage

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