How To Measure Investment Returns Vs Risks

In general, investment involves the commitment of funds to assets that will be held over a period of time. Investors (as opposed to speculators) would normally have time horizons that extend beyond a period of six months or a year. In making the decision to commit their funds for such a long period of time, they would wish to derive a reasonable return on their investments. The return that they can earn from investing in the various types of assets including stocks, bonds, derivative securities, property and others, is known as the Rate of Return. This return must compensate investors for:

1. opportunity costs of time, or time value of money;
2. expected inflation (which erodes purchasing power), and
3. the risk associated with the investment

Why do people invest? The simple answer to that is to make more money and to make money grow in value of course. In order to realize higher returns, investors must bear higher levels of risk. Therefore, underlying all investment decisions is the tradeoff between risk and return - the higher the risk, the higher the return.

How to calculate rate of return on investment? Consider the following scenario:
Beginning of year investment at cost = $1,000
End of year investment at market = $1,300
Holding Period Return (HPR) = Market / Cost = 1300/1000 = 1.3
Holding Period Yield (HPY) = 1.3 - 1 = 0.3 or 30%

To derive the return over the holding period, just take the HPR to the power of (1/n), where n being the number of years. Say if investment period is 18 months, n will be 1.5 year. Hence annualized HPR = 1.3 power of (1/1.5) = 1.19
annualized HPY = 1.19-1 = 0.19 or 19%

What then for a portfolio of stocks? Consider this scenario where there are three stocks in the portfolio:

Stock	No. of shares	Price (start)	Market Value (start)	Price (End)	Market Value (End)	HPR	HPY (%)	Market Weight	Weighted HPY
X	10,000	1	10,000	1.2	12,000	1.2	20%	5%	0.01
Y	20,000	2	40,000	2.1	42,000	1.05	5%	19%	0.01
Z	50,000	3	150,000	3.3	165,000	1.1	10%	75%	0.075
Total			200,000		219,000				0.095

From the above, we gather that the overall rate of return for this portfolio is therefore 9.5%.

For the less patient ones, the easier way to calculate this is by taking (219,000 minus 200,000) divided by 200,000 and one will get the same percentage return.

The above example is useful in calculating the realized rates of return on a portfolio of stocks, so that they can be compared to alternative investments. Nevertheles, in order to select investments for your portfolio requires you to predict the expected rate of return. This is not always so easy as it involves taking into account, factors such as the level of risk one is prepared to assume in undertaking the investments.

Let's proceed to compute the expected rate of return by taking the following scenario:
Based on one's prediction, supposed there is a 50% chance of hitting a 10% return, 30% chance of hitting a 20% return and a 20% of hitting a 50% return, the expected rate of return will be

(0.5*10%)+(0.3*20%)+(0.2*50%) = 21%

Now comes the more complicated part but important for risk measurement. We will now derive the variance which is a measure of the dispersion of the expected returns.
Variance = (0.5*0.1^2)+(0.3*0.2^2)+(0.2*0.5^2)-0.21^2 = 0.0229

The larger the variance, the higher the dispersion of expected returns, implies higher volatility for the investment.

Next, we compute the Standard Deviation (SD) which represents the degree of risk of the investment:
Standard Deviation = Square root of Variance = 0.0229^(1/2) = 0.15132746 Once again, the higher the standard deviation, the greater the risk of investment.

In some cases the variance or standard deviation, which is unadjusted, may be misleading – the Coefficient of Variation (CV) is designed to overcome this problem. It is a relative measure – the CV is derived by relating the standard deviation to the expected return, and thus indicates the risk per unit of expected return.

Consider the following scenario:
Stock A: SD = 0.01, ER (Expected Return) = 10%
Stock B: SD = 0.02, ER = 15%

The computation of the CV will be as follows: SD divided by ER
Stock A = 0.01 / 0.1 = 0.10
Stock B = 0.02 / 0.15 = 0.133

Hence, stock B has a higher risk per unit of expected return. Therefore for investors with lower risk appetite, Stock A appears to be a better choice of investment.

Do leave me a comment on your thoughts of using this method to evaluating investment risks vs return.