Chap 17 - Relative Value Hedge Funds Flashcards
Relative value strategies attempt to capture alpha through predicting changes inrelationships between prices or between rates. For example, rather than trying to
predict the price of oil, a relative value strategy might predict that there will be a
narrowing of the margin between the price of oil and the price of gasoline.
Relative value fund managers take long and short positions that are relatively equal
in size, volatility, and other risk exposures.
Profit can come from short positions in relatively overvalued securities and long positions in relatively undervalued securities, therefore their prices (valuations) converge to their equilibrium values in normal market conditions.
What is convergence ?
Convergence is the return of prices or rates to relative values that are deemed normal.
How does the classic relative value strategy trade works ?
The classic relative value strategy trade is based on the premise that a particular
relationship or spread between two prices or rates has reached an abnormal level and
will, therefore, tend to return to its normal level. This classic trade involves taking a
long position in the security that is perceived to be relatively underpriced and a short position in the security that is perceived to be relatively overpriced.
Performs well when decreasing volatility.
How does a classic convertible bond arbitrage work ?
The classic convertible bond arbitrage trade is to purchase a convertible bond that is
believed to be undervalued and to hedge its risk using a short position in the underlying equity. The hedge is usually adjusted as the underlying stock rises or falls in value. If the underlying equity experiences volatility that is higher than the volatility implied by the original market price of the bond, then the strategy generates favorable returns.
What are Convertible bonds ?
Convertible bonds are hybrid corporate securities, mixing fixed-income and equity
characteristics into one security. In their simplest form, convertible bonds can be
thought of as a combination of an unsecured corporate bond and a call option on the issuer’s stock.
What is the concept of moneyness ?
The characteristics of convertible bonds vary widely with the moneyness. Moneyness
is the extent to which an option is in-the-money, at-the-money, or out-of-the-money.
In the case of a convertible bond, moneyness indicates the relationship between the
strike price implied by the conversion option and the price of the underlying stock.
What are busted convertibles and do they work ?
Bonds with very high conversion premiums (see Equation 17.1) are often called busted convertibles, as the embedded stock options are far out-of-the-money. These
bonds behave like straight debt because when the stock option is far out-of-themoney, the convertible bond’s value is primarily derived from its coupon and principal payments.
What is a equity-like convertible and how do they work ?
Bonds with very low conversion premiums have stock options that are deep in-the-money, where the convertible bond price and the conversion value are very close.
The further in-the-money that the option is, the more the convertible bond behaves
like the underlying stock. An equity-like convertible is a convertible bond that is far
in-the-money and therefore has a price that tracks its underlying equity very closely.
Interest rates and credit spreads matter less on equity-sensitive convertibles.
What is a hybrid convertibles and how do they work ?
Convertible bonds with moderately sized conversion ratios have stock options
closer to being at-the-money and are called hybrid convertibles. Hybrids are usually
the most attractive bonds for use in convertible arbitrage strategies. These hybrid
convertibles are attractive for convertible arbitrage due to their asymmetric payoff
profile.
What is Delta ?
Delta is the change in the value of an option (or a security with an implicit
option) with respect to a change in the value of the underlying asset.
Call options that are very far out-of-the-money have deltas near 0.0, whereas options very far in-the-money have deltas near 1.0. The delta of a put option is negative. Delta is the first derivative of an option’s price with respect to the price of the underlying asset and is a key concept in setting the hedge ratio of a convertible arbitrage position.
What is Gamma ?
Gamma is the second derivative of an option’s price with respect to the price of
the underlying asset—or, equivalently, the first derivative of delta with respect to the
price of the underlying asset. That is, it measures how delta changes as the price of
the underlying asset changes.
Gamma is near zero when an option is extremely far out-of-the-money and the delta is very small. Gamma is also near zero when an option is extremely far in-the-money and the delta is near one. Gamma tends to be largest when the option is near-the-money.
What is Theta ?
It is the first derivative of an option’s price with respect to the time
to expiration of the option. Theta is negative for a long position in an option, since
as time passes and all other values remain the same, the option declines in value. In a
nutshell, theta reflects the loss in an option’s time value as time passes, which can be
referred to as time decay.
Delta is used to establish the hedge ratio in a traditional convertible arbitrage position. Gamma ensures that the hedged position will make money if the underlying asset quickly rises or falls in value. This profit is generated by the unlimited upside and limited downside nature of a long position in an option. Theta of the long option position indicates that as time passes, the hedged position
loses value in the absence of underlying asset changes. Thus, a traditional convertible arbitrage strategy’s return varies directly with the level of volatility experienced in the underlying asset.
What is a delta-neutral position ?
A delta-neutral position is a position in which the value-weighted
sum of all deltas of all positions equals zero. Example: convertible-bond with delta of 0.5. Long 1 convertible bond and short 0.5 shares, offsetting each other and leaving the combined positions insensitive to small changes.
If a large price change in the underlying asset takes place, the hedged position
makes a profit, and the positions are adjusted to being delta-neutral based on a new
hedge ratio at the new price levels. If the underlying stock price does not move, the
convertible bond will slowly decline to its par value at maturity, and the hedged
position will fall, illustrating the negative theta.
For the arbitrageur to make more money on gamma than is
being lost on theta, which is known as time decay, the stock must keep experiencing
substantial price changes. These price changes dictate the relationship between
realized volatility and implied volatility.
What is realized volatility ?
Realized volatility is the actual observed volatility (i.e., the standard deviation of returns) experienced by an asset.
What is implied volatility ?
The implied volatility of an option or an option-like position—in this case, the implied volatility of a convertible bond—is the standard deviation of returns that is viewed as being consistent with an observed market price
for the option.
The keys to convertible arbitrage success are to buy convertible bonds with underpriced conversion options (i.e., implied volatility that is too low), short sell convertible bonds with overpriced conversion options (i.e., implied volatility that is too high), and maintain hedges by taking offsetting positions in the underlying equity to control for risk.
What is a complexity premium ?
A complexity premium is a higher expected return offered by a security to an investor to compensate for analyzing and managing a position that requires added time and expertise.
What are the 2 arguments so that convertible bonds should consistently offer superior risk-adjusted returns ?
First, demand to buy convertible bonds must be restricted such that
it prevents convertible bond prices from increasing to the point of offering normal
risk-adjusted returns. Second, suppliers of convertible bonds (corporations) must be
of sufficient size to suppress convertible bond prices to the point of allowing superior
returns.
When does Dilution takes place ?
Dilution takes place when additional equity is issued at below-market values, and the per-share value of the holdings of existing shareholders is diminished.
What are The components of convertible arbitrage returns ?
The components of convertible arbitrage returns include interest, dividends, rebates,
and capital gains and losses.
In the traditional convertible arbitrage trade of being long the convertible bond, the larger and more frequent the stock price moves, the greater the profits from gamma trading. Profits from gamma trading, though, are offset through theta, or time decay. The goal of gamma trading is to earn more in profits from gamma than the option value loses in time decay. This goal is met when the realized volatility of the stock exceeds the implied volatility priced into the option on the day the convertible bond is purchased.
How can a delta hedge benefit from stock movements ?
Due to the nonlinear nature
of their payoff, most at-the-money convertible bonds exhibit a desirable property known as positive convexity, or high gamma. That is, they appreciate in value from an immediate upward stock price change more than they depreciate from the same sized downward change in the underlying stock price. This section shows that a delt-hedged position will actually benefit from any movement in the underlying stock due to this convexity.
Why is it useful to short-sell the equity in a delta hedge ?
The primary risk of holding a long convertible position comes from the potential variations in the underlying stock price. This equity risk can be easily eliminated by selling short an appropriate quantity of the underlying stock. This quantity corresponds to the convertible’s delta multiplied by the number of shares into which the bond may be converted.
Arbitrageur would need to sell short delta
times the conversion ratio (0.625 × 8=5.0) shares of stock per $1,000 face value
of the convertible bond bought.
What is a net delta ?
The net delta of a position is the delta of long positions minus the delta of
short positions.
How does the rebalance of a delta-hedge work ?
stock price +, the option moves in-the-money and the convertible bond becomes more equity sensitive. The delta increases, so the arbitrageur must adjust the hedge by shorting more shares.
stock price -, option ,moves out-of-the-money, the delta declines, and the arbitrageur must reducethe hedge by
buying back some shares:
For example, if the delta rises to 0.70 due to a stock price increase, the short
position must be expanded from 5.0 shares to 5.6 shares (8 × 0.70). If the delta falls
to 0.50 due to a stock price decrease, the short position must be contracted to 4.0
shares (8 × 0.50). The hedge needs to be rebalanced repeatedly as the stock price
moves, in a strategy known as dynamic delta hedging.
