Please help me in this question the one in bold i ahve been able to answer but t
ID: 2783553 • Letter: P
Question
Please help me in this question the one in bold i ahve been able to answer but the one just after it is what i have not been able to answer. I have provided the one with the bold one as some of the information will be needed to procced with the next question. Kindly help me in the next question will a detailed explanation along with all the appropriate reasoning.
Suppose that a portfolio is worth $60 million and the S&P 500 is at 1200. If the value of the
portfolio mirrors the value of the index, what options should be purchased to provide
protection against the value of the portfolio falling below $54 million in one year’s time? Also Suppose that the portfolio has a beta of 2.0,
the risk-free interest rate is 5% per annum, and the dividend yield on both the portfolio and
the index is 3% per annum. What options should be purchased to provide protection against
the value of the portfolio falling below $54 million in one year’s time?
Explanation / Answer
54 is 90% of 60. Means you need protection when market falls below 10% from 1200
So, you need to buy a put option which allows you to sell the S&P 500 at 1200-120 = 1080
In second case, since the portfolio beta is 2.0 it means it will move twice in the direction of the market, thus if market falls by 5%, the portfolio will fall by 10%. And hence, you need to buy a put option to sell S&P 500 below 95% of current levels i.e. 1140.