Question

Explain the return and risk relationship concept in finance.

Describe a situation whereby a department’s attitude is: Risk neutral, risk-averse or risk-seeking.

Explain and critically analyse the distinction between decision tree, expected value and maximax, maximin and regret criterion can be used for decision-making under conditions of risk and uncertainty. The managing director of Bounce Ltd has asked you to explain how each method of the above can be applied in decision-making and comment on the strengths and limitations of each method.

Answer 1

The risk and return relationship in finance states that an investor expects higher return for an investment which has greater amount of risk. These risks could be political risk, interest rate risks, liquidity risks or default risks. So typically an instrument having higher risks should provide an investor with a higher return to compensate the investor for taking on such a higher amount of risk.
A department is risk neutral wherein it only seeks to maximize the expected value of an investment. For example, an investor having risk neutral outlook would be indifferent between an investment having a 50% probability of return of $100 and 50% probability of return of $0 and a fixed payout of $ 50.
A risk seeking investor would be more kin to take on risks to get a higher return. So in the above case, a risk seeking investor would prefer the volatile investment which has a 50% probability of return of $100 and 50% probability of return of $0 than a fixed payout of $ 50.
On the other hand a risk averse investor would much rather have a fixed payout of $50 without any volatility and that investor would tend to reduce volatility in their investments.
A decision tree method can be used under uncertainty by calculating payoff for each state and then calculating probability for each payoff. Then through backpropagating the decision tree and eliminating the outcomes that are not optimal, the best decision is arrived at. The advanatge of this method is that it is an objective method backed by strong quantitiative calculations.
However, the disadvantage is that probbaility of each occurence has to be estimated in order to run this model and that might itself be difficult to estimate for the future.
The expected value criterion seeks to select the decision that maximize the expected value of the decision given various states of nature. This is also quite an objective method but it has the disadvantage of again having to estimate the probability of each state of nature which is not easy.
The maxi-max criterion seeks to select the decision, which provides the maximum outout under various states of nature. While this is a good method as it does away with the need to calculate the probabilities, it overestimates the output under each decision as it only takes into impact the maximum value of each decision.
The maxi-min criterion is a conservative approach wherein the decision is selected which maximizes the minimum value under each nature state. This method also is good as it do not have to calculate probability, but again this underestimates each of the output.
The regret criterion is one wherein the decision is selected which minimizes the maximum regret which is possible from taking any decision. It also do not involve calculation of probability, however it do not look at the potential gain instead looks to minimize losses which is an indication of risk averse outlook. So it may not be suitable risk taking or risk neutral investors.