The motivation for holding equity (and investment horizon) differs from investor to investor. The household sector (individuals) may hold equity for speculative reasons (short term horizon), to invest to earn a return for a special holiday planned for 5 years' time (medium term horizon), or for retirement reasons (long-term horizon).

Companies may hold equity in subsidiaries (long term) or, in the case of investment companies / trusts, for investment reasons on behalf of their shareholders (medium-term to long-term). The foreign sector may hold equity for a variety of reasons, such as long-term strategic holdings, making short-term capital gains, making a gain on the currency, or because the prices of local shares are inexpensive relative to their home equity market or other international equity markets.

Banks are small holders, and may also hold equity for a number of reasons, the main one being opportunistic profits (i.e. speculation). The contractual intermediaries and CISs, however, hold equity for long-term investment reasons. They are the custodians of much of the wealth of the nation, and because their funds under management increase continuously, they are permanent and increasing holders of equity.

In all the above cases, the other issue that influences decisions in respect of equity investment is of course the tax regime: tax rates and type of tax (capital gains, tax on dividends on investment vehicles and on individuals.

The common reason for all of the above holding equity is the return enjoyed in the long-term. Equities deliver superior returns relative to the other asset classes in the long-term. This significant issue is exploited in some detail later.

3.5. Statutory environment for investors

As noted above, the holders of equity may be categorised as follows:

• Ultimate lenders:

- Household sector.

- Corporate sector.

- Government sector.

- Foreign sector.

• Financial intermediaries:

- Banks.

- Investment vehicles:

• CIs

• CISs

• AIs.

The household sector (individuals) is not constrained by any statutes in terms of their investment in the equity market. The same applies to the corporate sector (in their case there will of course be internal controls in this regard). The government sector holds equities mainly in public enterprises and there are no constraints in this regard. The foreign sector will be constrained by statutes applying in their respective countries.

For the financial intermediaries, there is an extensive statutory environment. The banks are constrained by the capital and other requirements of the banking statute.

The contractual intermediaries and the CISs have constraints placed on their equity investments and exposures to single companies under the statutes that apply to them.

3.6. Measures of return

3.6.1. Introduction

Risk is ever-present in all financial markets, and there is a trade-off between risk and return. As such it is important to understand these concepts and how to measure them. We consider the sources of return and explain how to measure historical, average historical, and expected return, and then elucidate the concept of risk and how to measure risk.

There are various ways in which returns may be computed. Here we consider:

• Holding period return (HPR).

• Annualized HPR.

• Arithmetic mean return.

• Geometric mean return.

3.6.2. Holding period return

The sources of return are twofold:

• Income (dividends in the case of equity; interest in the case of the debt market)

• Change in price (capital gain or loss).

The time an investment is held is the holding period (HP); holding period return (HPR) is therefore:

HPR = (price change + income) / purchase price. This may also be written as:

HPR = [(Pt - P0) + I] / P0

where:

P0 = purchase price of share P1 = selling price of share I = income amount.

The HPR in the case of debt instruments is the same as above but with the prices being the all-in prices: HPR = [(AIP1 - AIP0) + I] / AIP0.

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3.6.3. Annualised HPR

Individuals calculate the HPR of an investment for the period over which it was held; thus this measure of return is rarely an annual return. The annual return is captured in the Annualised HPR:

For example, if the HP in the example in the previous section was 2 years, the Annualised HPR is (n = number of years; less that a year = months / 12):

Similarly, if the HP in the example above was 6 months, Annualised HPR is:

Annualised HPR = (1 + HPR)1/n -1

= (1 + 0.25)1/(6/12) - 1 = (1 + 0.25)2 - 1

= 0.5625 = 56.25%.

3.6.4. Arithmetic mean return

Other measures used in the financial industry are the arithmetic mean return (AMR) and geometric mean return (GMR). These are used to measure average returns over a number of years (n), because in some years returns are negative while in other years returns are positive.

The arithmetic mean return (AMR) is (Z = Greek sigma = sum of):

AMR = Z HPR / n

An example (non-dividend-paying share) is presented in Table 2.

Share price

Share price

Start of year 1

LCC20.0

End of year 1

LCC0.0

LCC25.0

0.25

End of year 2

LCC0.0

LCC20.0

-0.20

0.025 or 2.5%

Table 2: Example of mean return

HPR (end of year 1) = [(P1 - P0) + I] / P0

= [(25.0 - 20.0) + 0.0] / 20.0 = 5.0 / 20.0

= 0.25

HPR (end of year 2) = [(P1 - P0) + I] / P0

= [(20.0 - 25.0) + 0.0] / 25.0 = -5.0 / 25.0

= - 0.20

AMR = Z HPR / n

= [0.25 + (-0.20)] / 2

= 0.025

= 2.5%.

The problem here will be apparent: even though the investor earned zero return over the period of two years, this calculation says that the investor earned an average annual return of 2.5%.

3.6.5. Geometric mean return

The correct method to determine the annual rate of return over a number of periods (such as years) is the geometric mean return (GMR). Using the same example, the GMR is:

GMR = [n(1 + HPR)]1/n -1

= [(1.0 + 0.25) x (1.0 - 0.20)]1/2 -1 = (1.25 x 0.8)0.5 -1

= 0.0.

This says that the GMR is the nth root of the product (n) of 1 + HPR for n years. It will be clear that the GMR measure is accurate, while AMR is considered a "rough" indicator.

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