Q1. Suppose you are managing a stock portfolio that is currently valued at $2,00

Question

Q1. Suppose you are managing a stock portfolio that is currently valued at $2,000,000. You expect the stock market will be bullish in the next 6 months. But you are also aware of a small chance of market crash and you want to insure that your portfolio value will be at least $1,800,000 in 6 months even in a market crash. In other words, you don’t want to suffer more than 10% loss in the next 6 months. Assume your stock portfolio has a beta of 1.5, the current S&P 500 level is 2,000 and the risk-free rate is 1% per annum.

How would you hedge against your portfolio value dropping below $1.8M in 6 months? Be specific with your strategy. If you are using options, specify what the underlying asset is, the strike price, time to expiration. whether it’s a call or a put and how many units to buy or short.

Explanation / Answer

We will hedge our portfolio by going long on a put option i.e. buying a right of sell our portfolio or similar underlying asset at a strike price which will minimize our losses to 10%.

First since our portfolio will be diversified it will be diffult to have put option which individual stocks as underlying asset. So in this case we will have S&P 500 stock as our underlying asset.

Now we will see how this market stock will behave in case their is 10% loss in our portfolio stock i.e. Portfolio rate of return Rp=-0.1.

Risk Free Rate, Rf=1%=0.01 & Beta is 1.5. So we can calculate Rm(S&P rate of return)

Rp=Rf+Beta(Rm-Rf) --- CAPM model

So by puting the respective values we will solve for Rm which comes out to be -0.105 or 10.5% so if the markets fall for 10.5% then our portfolio will experience 10% loss & vice versa.

Currently the index is at 2000 so 10.5% fall will result in its value as 1790.

So the Strike Price of the Put option on which we go long will be 1790 with the time to expiration as 6 months from now. Now no. of such put options we will have to buy will depend on the no. of stocks in 1 option. Let us assume that each put options gives us right to sell 100 S&P 500 stocks. So as currently S&P 500 is at 2000, in order to cover our $2 million portfolio we will have to buy 20,000 put options.

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