CFAI 2014 Mock PM C – Allison Q1

Question

@RaviVooda‌ @Alta12‌

Hi guys, not too sure if you have done this question.

The text:
"Client A has a $20 million technology equity portfolio. At the beginning of the previous quarter, Allison forecasted a weak equity market and recommended adjusting the risk of the portfolio by reducing the portfolio’s beta from 1.20 to 1.05. To reduce the beta, Allison sold NASDAQ 100 futures contracts at $124,450 on 25 December. During the quarter, the market decreased by 3.5%, the value of the equity portfolio decreased by 5.1%, and the NASDAQ futures contract price fell from $124,450 to $119,347. Client A has questioned the effectiveness of the futures transaction used to adjust the portfolio beta."

The question:
￼1.) With respect to Client A, Allison's most appropriate conclusion is the futures transaction used to adjust the beta of the portfolio was:
A. ineffective because the effective beta on the portfolio was 1.27. 
B. effective.
C. ineffective because the effective beta on the portfolio was 1.64.
Answer = A

The effective beta is the (hedged) return on the portfolio divided by the return on the market. The return on the market is –3.5%. The return on the portfolio is –5.1% plus the return on the futures position. The return on the (short) futures position relative to the unhedged portfolio is –25 × (119,347 – 124,450)/20,000,000 = +0.0064. Effective beta = (–0.051 + 0.0064)/–0.035 = 1.27.

My question:
Where did the solution obtain the -25 contracts from?

vincentt · Answer

@alta12 thx mate but what formula is this?
No. of nasdaq futures required to short = 1.05 - 1.2 ($20,000,000/ $124,450) = -24

I thought it would be:

(target beta - portfolio beta) / future beta  * (portfolio value / contract price) ?

But we were not given NASDAQ's future beta?

Alta12 · Answer

@vincentt‌

No. of nasdaq futures required to short = 1.05 - 1.2 ($20,000,000/ $124,450) = -24

Value of portfolio = $20,000,000 x (1 - 0.051) = $18,980,000
Value of short position = 24 x ($124,450 - $119,347) = +$122,472
Portfolio Value = $19,102,472

Portfolio Beta = ($19,102,472/ $20,000,000) - 1 = -0.04488

Effective Beta = -0.04488/ -0.035 = 1.28 (A)

I got confused at first as I thought she sold 100 futures. Not sure if this happened to you too.