Investment Performance Analysis

• Topic 01

  Investment Performance Analysis

  90 questions

A few questions from this unit, with the answer and a full explanation. The complete bank is available when you start practising.

1. Why is duration always less than or equal to maturity for a coupon-paying bond?

   • A
     Because coupons reduce the present value of the redemption payment, making the maturity date irrelevant
   • B
     Because coupon payments are received before maturity, pulling the weighted average time of all cash flows earlier than the final maturity date
     Correct answer
   • C
     Because duration measures uncertainty rather than time, and uncertainty is typically lower than the remaining time period
   • D
     Because the bond's yield reduces the effective number of years the investor is exposed to price risk
   Explanation

   Macaulay duration is the weighted average time to receive all cash flows from a bond. For a coupon bond, cash flows arrive at each coupon payment date (typically semi-annually or annually) before the final redemption at maturity. The coupon payments received in early periods 'pull' the weighted average time forward, making duration shorter than maturity. Only a zero coupon bond (with one single cash flow at maturity) has duration equal to maturity. The higher the coupon rate, the more cash is received early, and the shorter the duration relative to maturity.

2. A callable bond is priced at £98 with a call price of £100. Yields fall by 2%. A standard bond of identical maturity and coupon rises to £104. What is the approximate price of the callable bond?

   • A
     £104, because the yield decline applies equally to callable and non-callable bonds
   • B
     £96, because the callable feature reduces the bond's value when rates fall
   • C
     Approximately £100, because the call price creates a ceiling; the bond is unlikely to trade significantly above £100 as the issuer will call it
     Correct answer
   • D
     £102, because the callable bond captures half the price gain of the equivalent non-callable bond
   Explanation

   When a callable bond's price approaches its call price, market participants anticipate the issuer will exercise the call option to refinance at lower rates. The bond's price is therefore limited to approximately the call price (plus any accrued interest). Even though the equivalent non-callable bond would trade at £104 following the yield decline, the callable bond trades near £100 — this price compression relative to the non-callable bond is the economic manifestation of negative convexity. The investor bears the reinvestment risk when the call is exercised.

3. A pension fund has consistently beaten its peer group benchmark by 1% per annum. The trustee proposes to switch to a liability benchmark. How might this change the apparent performance outcome?

   • A
     The trustee would need to maintain both benchmarks and report the better result to members under FCA COBS 14 requirements
   • B
     The liability benchmark shows better performance than a peer group benchmark because liabilities grow more slowly than equity markets over the long term
   • C
     If liabilities have grown faster than the portfolio (e.g., due to falling interest rates), switching to a liability benchmark could show negative performance even though the fund beat its peer group
     Correct answer
   • D
     Switching to a liability benchmark would make no difference because all benchmark types produce the same relative performance ranking for the same portfolio
   Explanation

   The two benchmarks measure fundamentally different things. A peer group benchmark asks: 'did we do better than similar funds?' A liability benchmark asks: 'did the assets keep pace with the liabilities?' If interest rates have fallen sharply, liabilities may have grown by 15% while the portfolio returned 10% — good relative to peers, but bad relative to liabilities (funded status has deteriorated). For a DB scheme, the liability benchmark is the more economically meaningful measure of whether the scheme is meeting its obligations to members.