# LO 6.3: Describe the structure, uses, and payoffs o f a correlation swap.

LO 6.3: Describe the structure, uses, and payoffs o f a correlation swap.
A correlation swap is used to trade a fixed correlation between two or more assets with the correlation that actually occurs. The correlation that will actually occur is unknown and is referred to as the realized or stochastic correlation. Figure 6 illustrates how a correlation swap is structured. In this example, the party buying a correlation swap pays a fixed correlation rate of 30%, and the entity selling a correlation receives the fixed correlation of 30%.
Figure 6: Correlation Swap with a Fixed Correlation Rate
Fixed rate p Payer
Fixed p = 30% ———————-
:————–
Realized p
Selling Correlation Fixed rate p Receiver
The present value of the correlation swap increases for the correlation buyer if the realized correlation increases. The following equation calculates the realized correlation that actually occurs over the time period of the swap for a portfolio of n assets, where pj. is the correlation coefficient: realized P
realized
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The payoff for the investor buying the correlation swap is calculated as follows:
Topic 6 C ross Reference to G A R P A ssigned R eading – M eissner, C h apter 1
notional amount x (p pc , pc vr realized
,) r fixed’
Example: Correlation swap
Suppose a correlation swap buyer pays a fixed correlation rate of 0.2 with a notional value of $1 million for one year for a portfolio of three assets. The realized pairwise correlations of the daily log returns [ln(St / 5t_j)] at maturity for the three assets are p2 ^ = 0.6, p3 l = 0.2, and p3 2 payoff? = 0.04. (Note that for all pairs i > j.) What is the correlation swap buyers Answer: The realized correlation is calculated as: Prealized = 7^ 7 x 3 3 + 0-04) = 0.28 The payoff for the correlation swap buyer is then calculated as:$1,000,000 x (0.28 – 0.20) = \$80,000
Another example of buying correlation is to buy call options on a stock index (such as the Standard & Poors 500 Index) and sell call options on individual stocks held within the index. If correlation increases between stocks within the index, this causes the implied volatility of call options to increase. The increase in price for the index call options is expected to be greater than the increase in price for individual stocks that have a short call position.
An investor can also buy correlation by paying fixed in a variance swap on an index and receiving fixed on individual securities within the index. An increase in correlation for securities within the index causes the variance to increase. An increase in variance causes the present value of the position to increase for the fixed variance swap payer (i.e., variance swap buyer).
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