CFA CFA Level 3 CFAI 2014 Mock PM C – Allison Q1

CFAI 2014 Mock PM C – Allison Q1

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    • vincentt
      Participant
        • CFA Level 3
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        @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
        Participant
          • CFA Level 3
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          @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?

        • Up
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          @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.

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          Beta for futures to assumed to be = 1 if not given otherwise.

          Your formula above is the right one.

        • vincentt
          Participant
            • CFA Level 3
            Up
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            @alta12 thanks for that, hmm i wonder if schweser really did not mention that because it will always be given or I must have missed it. Just like the duration of a swap is 75% of the remaining maturity. Thanks again!

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