A correlation swap based on five assets has a notional value of $1.7 million and a strike correlation rate of 0.35. The market weights of the assets are equal. Four of the assets have realized return correlations between each other of 0.62; one of the assets has no return correlations with the other four assets. Which of the following comes closest to the net swap payment to be made to the swap buyer?
Five assets: A, B, C, D, E. Ten realized correlations: AB, AC, AD, AE, BC, BD, BE, CD, CE, DE. If one asset (say A) has no return correlations with the other assets (so remove any pairing with asset A from the list), that gives 4 zero correlations and leaves 6 non-zero correlations.
Since the asset weights are equal, the average realized correlation is: [(0.62 × 6) + (0 × 4)] / 10 = 0.372.
Swap payment = Notional value × (Avg. realized correl.− Strike correl.)
= $1.7m (0.372 − 0.35) = $37,400
Since the payment is positive, it is made to the swap buyer (by the swap seller).
This question refers to material in T7-Ch30-LO4.
My question is why do you multiple 0.62 (correlation fo 4 assets) time 6?