Question

Suppose the rate of interest on borrowing is higher than the rate of interest at which you can lend. Illustrate and explain the implications for the efficient frontier, and also for portfolio selection decisions where investors have the same information but differing degrees of risk aversion. No calculations are necessary in this section.

Answer 1

There is no set risk-free rate, but there is a generally accepted ceiling that can be earned without taking any significant risk. There is however the unfortunate opportunity of earning 0% as your own personal risk-free rate.

In a mean-variance framework, the selected risk-free rate will have some bearing on the optimal portfolio and will affect the resulting mix of this portfolio and the risk-free asset. These effects have been most pronounced when the risk-free rate is higher.

With rates still low from a historical perspective, the impact of not achieving the full risk-free rate may not be extreme, but with how simple it is to deploy cash in a more effective manner, setting up a process in the current increasing rate environment is a sensible way to maximize returns in a guaranteed way when other assets are facing headwinds of uncertainty.

The efficient frontier is the set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the efficient frontier are sub-optimal because they do not provide enough return for the level of risk.Portfolios that cluster to the right of the efficient frontier are sub-optimal because they have a higher level of risk for the defined rate of return.the efficient frontier rates portfolios (investments) on a scale of return (y-axis) versus risk (x-axis). Compound Annual Growth Rate (CAGR) of an investment is commonly used as the return component while standard deviation (annualized) depicts the risk metric. The efficient frontier graphically represents portfolios that maximize returns for the risk assumed. Returns are dependent on the investment combinations that make up the portfolio. The standard deviation of a security is synonymous with risk. Ideally, an investor seeks to populate the portfolio with securities offering exceptional returns but whose combined standard deviation is lower than the standard deviations of the individual securities.1 The less synchronized the securities (lower covariance) then the lower the standard deviation. If this mix of optimizing the return versus risk paradigm is successful then that portfolio should line up along the efficient frontier line.

An equity stock providing high returns may be suitable for one investor but another investor may want to avoid such an investment. This happens because of the different attitudes of investors towards risk. A portfolio manager will consider the risk profile of his client investors and try to match his portfolio investment in such financial instruments that have the similar risk-return profile.

This concept is called risk aversion. In general, risk aversion refers to the behaviour of investor to prefer less risk to more risk. A risk averse investor will:

• Prefer lower to higher risk for a given level of expected return
• Accept high risk investment only if expected returns are greater

Risk Neutral Investor

A risk neutral investor is someone who is only concerned about the return but does not worry about the risk posed by the investment. As long as an investment provides high returns, this type of investor will go for it. In our example, a risk-neutral investor will be indifferent between the two choices. He will look at both choices 1) $100 for sure, and 2) 50% nothing and 50% $200, as the same. In general, investors are not risk neutral. An investor may be risk neutral if the investment is not so significant. For example, a very wealthy investor will be indifferent to whether he receives $100 guaranteed or goes for the gamble.

Risk Averse Investor

As we mentioned earlier, most investors are risk-averse, that is, they want to reduce the amount of risk they take for a given level of return. If the returns provided are higher, they will be willing to take proportionately higher risk. In our example, such an investor will go for guaranteed $100. In fact, depending on his risk aversion, he may even be willing to accept slightly lower returns (say $90 instead of $100) for the certainty he gets. Different investors will exhibit different degrees of risk aversion. In the figure above, the two investors IP and IQ have different levels of risk aversion. Investor IP is more risk averse than investor IQ as investor IPdemands more return for every additional unit of risk in the investment.

Risk Lover/Risk Seeker

The third category of investor is a risk lover. In our example, such an investor will choose to gamble because it’s not about the returns. Rather he loves taking risk, and gets additional pleasure by taking the risk. A risk lover definitely wants to increase his returns but his utility (level of happiness) increases from the extra risk that he takes. For risk lovers, the risk-return curve slopes downwards, i.e. the return they receive reduces and the risk increases. This is the typical profile of a gambler.