Question

5. Construct an indifference curve for 3 portfolios with different risk-return profiles

Answer 1

Indifference Curve
It is a curve that represents all the combinations of goods that give the same satisfaction to the consumer. Since all the combinations give the same amount of satisfaction, the consumer prefers them equally. Hence the name Indifference Curve.

Utility is a measure of relative satisfaction that an investor derives from different portfolios. We can generate a mathematical function to represent this utility that is a function of the portfolio expected return, the portfolio variance and a measure of risk aversion.

U = E(r) – ½Aσ2

Where

U = utility

E(r) = portfolio expected return

A = risk aversion coefficient

σ2 = portfolio variance

In determining the risk aversion (A), we measure the marginal reward an investor needs in order to take on more risk. A risk-averse investor will need a high margin reward for taking on more risk. The utility equation shows the following:

• Utility can be positive or negative – it is unbounded.
• High returns add to utility.
• High variance reduces utility.
• Utility does not measure satisfaction but can be used to rank portfolios.

The risk aversion coefficient, A, is positive for risk-averse investors (any increase in risk reduces utility), it is 0 for risk-neutral investors (changes in risk do not affect utility) and negative for risk-seeking investors (additional risk increases utility).

For analysis of choice of a portfolio of assets by individuals or firms we require to explain the concept of risk-return trade-off function which are represented by indifference curves between degree of risk and rate of return from investment.

The theory of choice under risk and uncertainty is also applicable in case of an investor who has to invest his savings in various types of assets having varying degrees of risk to get optimum return from them.

For instance, if an investor does not want to bear risk at all he may go in for investing in Fixed Deposits of the State Bank of India which carry a fixed rate of interest. If he is prepared to take risk he may be interested in buying shares from the stock market whose value and dividend can vary a good deal.

The indifference curve between expected income or return (measured along the vertical axis) and the degree of risk (measured by standard deviation and shown on the horizontal axis). Each indifference curve or what is also called risk-return trade off curve shows all those combinations of degree of risk (i.e. standard deviation) and expected return that give the individual same level of utility.

As riskiness is ‘bad’ or undesirable and therefore more of it yields less satisfaction and therefore as we move rightward indicating greater risk or standard deviation of the variability of return, the investor should receive higher expected return to give him equal utility or satisfactions. Therefore, indifference curves (i.e. risk – return trade off curves) between degree of risk and expected return slope upward (i.e. are positively sloped).

The concept of indifference curve or risk-return trade-off function can be better explained with Fig. 17.10 where on the X- axis, we measure risk in terms of standard deviation (σ) of probability distribution, and rate of return as per cent of investment is measured along the Y-axis.