Mr Woolly is choosing between two possible investment opportunities:
a. A government bond which will mature in exactly one year and on that date the nominal amount (£100) and a 3% interest payment will be made. The price of £100 nominal of this stock is £98 today.
b. 100 shares costing 98p each in a company specialising in software for personal computers. The return on the shares is uncertain but the investor has read a report on the company which estimates the one-year return to be as follows, subject to how the economy behaves and how the company's products are received by the market:
|Reception of ...view middle of the document...
The expected return on the share is 11.5% pa, calculated as follows (see p57 for full explanation):
|Return |Probability | |
|r |p |r x p |
|30% |0.2 |0.060 |
|15% |0.3 |0.045 |
|10% |0.3 |0.030 |
|-10% |0.2 |-0.020 |
|Expected return |0.115 |
| |or 11.5% |
The risk of the shares, as measured by the standard deviation of returns, is 12.855%, calculated as follows:
|Return |Dispersion |Square of dispersion |Probability of | |
| | | |return | |
| |Ri – E(R) |(Ri – E(R))2 |pi |(Ri – E(R))2pi |
|30% |18.500% |0.034225 |0.2 |0.0068450 |
|15% |3.500% |0.001225 |0.3 |0.0003675 |
|10% |-1.500% |0.000225 |0.3 |0.0000675 |
|-10% |-21.500% |0.046225 |0.2 |0.0092450 |
|Variance | |0.0165250 |
Solution to Exercise 1(ii)
The Fisher equation (p50) states that:
(1 + nominal rate) = (1 + real rate)(1 + inflation rate)
(1 + nominal rate)/(1 + inflation rate) = (1 + real rate)
[(1 + nominal rate)/(1 + inflation rate)] - 1 = real rate
So the expected real rate of return on the bond is:
And the expected real rate of return on the shares is:
The government bond is therefore expected to yield a negligible real rate of return, so that if actual inflation exceeds forecast by even a very small margin, the real rate of return will be negative. The shares are expected to yield nominal and real rates of return of 11.5% and 6.19% respectively, but with a standard deviation of nearly 13% there is more than a one-in-six chance that the nominal return will be negative and the real rate of return will be worse than -5%. Ultimately, the advice to Mr Woolly must be based on an assessment of his own utility curve and on his appetite for risk.
Solution to Exercise 1 (iii)
One key factor,...