Investment risk
Investment risk

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Investment risk

3.7 Interest rate risk

This has to be seen in conjunction with the previous comments about the secondary market in shares and debt instruments. An efficient secondary market can ensure that there is always a ready buyer for an investment, but the price at which the investment can actually be sold will depend entirely on market conditions at the time of sale. The secondary market price will not necessarily bear any relation to the price originally paid by the investor. The following example illustrates the general principle.

The Treasury Bill (‘T-bill’ for short) is a short-term IOU issued by the government and is the nearest approximation to a risk-free investment in the real world. It does not pay a separate contractual rate of interest, but is sold to the investor at a discount to its face value so that the investor achieves the agreed rate of return – if he holds the T-bill to maturity.

Investor A buys a 3-month T-bill with a face value of £1,000 at a discount to yield 8% p.a. (roughly equivalent to 2% for 3 months, i.e. ignoring the effect of quarterly compounding [1.024 = 1.0824, or 8.24%]). The amount she actually pays for the T-bill will therefore be £980.39, because 2% of that amount is £19.61, and £980.39 plus £19.61 is £1,000 exactly – the amount she will receive from the Treasury when it repays the face value on maturity. One advantage of T-bills as investments is that because they are so short-term and of such high quality, they can be traded at any time on the secondary market. After just a month – one-third of the way through the three months – investor A wants to realise her investment. Unfortunately, short-term interest rates have shot up in response to some unforeseen economic crisis, and investors now require a return of 12% p.a. from short-term loans to the government. How much will Investor A get for her T-bill on the secondary market? A new investor (Investor B) will pay only an amount which gives him a return of 12% per annum. Unfortunately, 12% per annum for a T-bill is equivalent to 2% for two months, so Investor B's arithmetic is exactly the same as Investor A's original calculation. He will be prepared to pay only £980.39 – precisely the same amount as Investor A paid a month earlier – because he needs an extra £19.61 on maturity to give him the required return of 12% per annum over the remaining two months.

So Investor A has paid a heavy price for the benefit of secondary market liquidity. She invested £980.39, and received just £980.39 on liquidation of her investment a month later. Effective rate of return for one month – zero % p.a.!

Self-assessment question 2

An investor purchases a newly issued 3-month T-bill with a face value of £5,000 at a price calculated to yield 6% p.a. to maturity of the bill. Interest rates subsequently fall sharply, and after exactly two months the investor sells the T-bill at a price that will yield 4% p.a. for the remaining period to maturity.

  1. How much did the investor pay for the T-bill, and how much did the investor receive on selling it? As in the example above, ignore compounding effects.

  2. What annual percentage rate of return did the investor achieve over the two-month holding period?

Answer

1. The original price paid is the amount on which the sum of £5,000 received after three months will represent repayment of principal plus interest at 6% p.a., which is (for T-bills) 1.5% for three months.

If we let P0 = the price paid, then:

£5,000 = P0 × (1 + 0.015)

Rearranging the equation with P0 on the left, we get:

P0 = £5,000 / (1 + 0.015)

     = £4,926.11

If we let P1 = the price received on sale of the T-bill at a yield of 4% p.a. with only one month to run to maturity (approximately 4/12 = 0.3333% for 1 month), then:

P1 = £5,000 / (1 + 0.003333)

     = £4,983.39

2. The investor's annual percentage return on holding the T-bill for two months is:

(P1P0) / P0 × 12/2 × 100 = 6.98% p.a.

i.e. {[4,983,39 − 4.926.11) / 4926.11] × 6} × 100

(For a T-bill the annual rate is 6 times the return over 2 months.)

By holding the T-bill during a period when interest rates fell, the investor has significantly enhanced the originally expected yield of 6% p.a. (to around 7%).

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