# derivatives question

I saw this on a non cfa context, but appears to be related to the cfa topic.

Im curious if anyone could help me understand the solution.

Thanks

The value of a portfolio is 33600. The s&p 100 is 212.50 The portfolio manager buys 2 s&p 100 sept 210 puts. What is the beta of the portfolio?

I dont want to give the answer supplied, because Im not sure its correct.

Thanks

was that all the information given?

That was it.

I presume it has something to do with the value of the puts he is buying vs the portfolio. Puts = 200*210 = \$42,000 / \$33,600 = 1.25.

Making the assumption that he is looking to completely hedge the portfolio downside and that the S&P100 is an approporiate measure of the market risk that the portfolio has assumed.

Your answer is the one they got but im curious how you got it.

I was trying to use the beta adjustment with futures formula, which uses addition/subtraction.

(1) Assume that the S&P 100 is a market proxy - market has a beta of 1 --> Cov(m,m)/Var(m) = 1

(2) Given that the market has a beta of 1 - the face value of the puts he has invested in is a multiple of the portfolio…the additional leverage in the puts therefore matches the beta of his portfolio - if we believe the assumption that he is completely hedging.

Agree with (1)

(2) (agree with )Given that the market has a beta of 1 - the face value of the puts he has invested in is a multiple of the portfolio…

the additional leverage in the puts therefore matches the beta of his portfolio - if we believe the assumption that he is completely hedging. (thinking of the puts have a greater hedging than that of the portfolio.

Am I wrong here? this is what im thinking…

Beta(target)Value(target)= Beta(portfolio)Value(portfolio) +beta(futures)*number*Multiplier*Price(futures)