Assume that you manage a $2 million portfolio that pays no dividends and has a beta of 1.25 and an alpha of 2% per month.Also, assume that the risk-free rate is 0.05% (per month) and the S&P 500 is at 1,300.If you expect the market to fall within the next 30 days, you can hedge your portfolio by ______ S&P 500 futures contracts (the futures contract has a multiplier of $250).

Question

Quizplus · Accepted Answer

To hedge a portfolio, we need to take a position in the opposite direction of how we believe the market will move. If we expect the market to fall, we need to sell S&P 500 futures contracts to profit from the price decline. We can use the following formula to calculate the number of futures contracts needed:

Number of contracts = (Portfolio beta x Portfolio value) / (Futures price x Futures multiplier)

Portfolio beta = 1.25
Portfolio value = $2 million
Futures multiplier = $250
Risk-free rate = 0.05%
Market return = 0% (since we expect it to fall)

We first need to calculate the expected excess return of the portfolio:

Expected excess return = Alpha + Beta x (Market return - Risk-free rate)
= 2% + 1.25 x (-0.05% - 0%)
= 1.75%

We can now use the following formula to calculate the futures price:

Futures price = Spot price x (1 + Risk-free rate - Expected excess return)^(Days/365)

Spot price = 1,300
Days = 30

Futures price = 1,300 x (1 + 0.05% - 1.75%)^(30/365)
= 1,279.34

Finally, we can calculate the number of contracts needed:

Number of contracts = (1.25 x $2,000,000) / (1,279.34 x $250)
= 7.75

We always round up the number of contracts to avoid under-hedging the portfolio. Therefore, we need to sell 8 S&P 500 futures contracts to hedge our portfolio. The correct answer is B.

Assume That You Manage a $2 Million Portfolio That Pays