CH13 - Relationship between returns

Question 1

Required return formula

Answer 1

required risk-free real rate of return +
expected inflation +
risk premium

The return that investors, as a whole, require on any asset class. The terms on the right-hand side represent market averages as investors are considered as a class here.

This makes sense if we consider that investors will require:
- that the value of their investments do not decrease in real terms
- additional compensation over and above this in return for giving up the use of the cash that they invest over the period of investment.
The risk premium then reflects the compensation required for the risk (that either of the above requirements may not be fulfilled) that investors incur by undertaking the investment.

Question 2

Expected return formula

Answer 2

1. initial income yield + expected capital growth
   2(approx). initial income yield + income growth + impact of change in yield

The expected return is what the investor expects to achieve on the asset, given the:

• price paid for the asset, and
• the price for which the investor expects to sell / redeem the asset, and
• the expected income whilst the asset is held.

Question 3

Required return vs expected return

Answer 3

If assets are fairly priced, required and expected returns will be equal.
By comparing the estimates of the two figures, an investor can determine whether or not an investment or asset class appears to be good value.

Question 4

Returns on equities

Answer 4

Over the long term, equity dividend growth might be expected to be close to growth in GDP, assuming that the share of GDP taken by ‘capital’ remains constant.

Equities would therefore be expected to give a real return close to the growth in real GDP plus the equity yield.

Question 5

Returns on fixed-interest bonds

Answer 5

For fixed-interest stocks there is no income growth. The initial yield and the capital value change for a bond held to redemption combine to give a fixed nominal total return, called the gross redemption yield.

However, if index-linked bonds are sold before redemption then the actual real return will depend on the price for which the bonds are sold. This will be influenced by the normal supply and demand issues.

Question 6

Returns on index-linked bonds

Answer 6

The real return on index-linked bonds is known at outset, if they are held to redemption. This real yield is often taken as the benchmark required real yield for the analysis of expected returns on equities.

Question 7

Returns on cash

Answer 7

Returns on cash might be expected to exceed inflation except in periods where inflation is rising rapidly and is under-estimated by investors.

Question 8

Risk premium

Answer 8

The risk premium on a particular asset class will depend on the characteristics of the asset and investors’ preferences, which will be largely driven by their liabilities. A higher return would be required from riskier asset classes. The risk premium in the equation above may cover any adverse feature of one investment relative to another for which investors require compensation.