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+1 vote
in BUS 4027W - Actuarial Risk Management by (200 points)
What is the most intuitive way to differentiate between an investor's required return and expected return? This was discussed in the tut but it's still a bit unclear. As I understand it, the required return is almost like a benchmark that must be met to undertake an investment, while an expected return is the actual return that the investor thinks the asset will generate. Is this correct?

2 Answers

+1 vote
by (1k points)
I pulled some definitions that helped me understand it.

The required rate of return on an investment can be though of as the "absolute minimum return on investment you would accept for that investment to be worthwhile." This has to be specific to the investor and their risk preferences (as well as their expectation of future inflation).

"The expected rate of return is the return on investment you expect to collect when investing in a stock." This rate is informed by the particular characteristics of the stock (the stock's history, price volatility, company particulars...).

So I think that your interpretation sums it up quite well.
+1 vote
by (2k points)
The idea of using a benchmark as an intuitive tool is not that useful in explaining the above concepts, because:

1. investment objectives are best phrased in economic terms and not by referring to asset class returns

2. a benchmark might be an overall average of some asset classes (e.g. 60% equity index and 40% bond index), while the arguments apply to asset classes one at a time (admittedly in the presence of the other asset classes)

A.mabaso has the right idea and I've added a full explanation below to fill in all the technical bits:

First let's start with the \underline{required return} on an asst. As an example, we can consider someone who wants inflation-beating returns over a 10-year period. We first check if this is a reasonable objective.

In this case it is, since the investment market offers risk-free inflation-linked bonds (which acts as a 'least risk' asset in this case). Now we look at all the other available asset classes: cash, bonds, equity, and some others.

Let's take equity as another example: we note that equity is very volatile and not guaranteed to beat inflation (or indeed inflation-linked bonds) over a 10-year period. For the investor to consider investing in equity, he/she would require average equity to give inflation-linked bonds returns plus a premium. It is a risk-based requirement.

This premium would be particular to each investor, but would depend on their risk aversion and time horison, among others. This premium may or may not be available in the market: \textbf{the required return is the expected average return that the investor would require, given the assumed volatility and other risk (we imagine the investor to view equity to behave according to some model, e.g. a log-normal model).}

Taking cash, for example, is very liquid, secure and not very volatile, so the investor might require a much smaller risk premium above inflation-linked bonds to consider a cash investment. Someone who is risk-seeking might require no equity risk premium or even be happy with a negative equity risk premium.

\underline{Expected return}\textbf{ is the return that an investor expects an asset class to give, on average.} As an example, our investor from above might require a 12% return from equity, but could also look at the equity market and expect a dividend yield of 4% and growth of 6%, for a total of 10%. In this case it is unlikely that the investor would invest in equity because his/her required return (12%) is lower than the expected return (10%) on this investment.

How this is calculated depends on the investor. Investors base their investment objectives partly on observed historic achieved returns (e.g. one would not have inflation-beating investments as a goal it if was never achieved in the past), and then base their required return from different asset classes on the risk-characteristics of those asset classes. Expected return is one's best estimate of what the class will deliver over the next time period, irrespective of one's requirement.

\underline{To illustrate the links to FinEco's}

The students might recall the separation theorem from FinEco's, under the CAPM section: we used asset expected returns (we assumed everyone had the same expectation, but in ARM we allow them to have different expectations) and covariances to build an efficient frontier. As a separate step, indifference curves then helped us pick the right portfolio for the investor. In the ARM formulation, indifference curves are specified by required returns.

Some investors would not include cash in their portfolios while other would think it is a bargain. Similarly, some would not include equity, while other would see it as a no-brainer to invest. \textbf{Market prices are determined by marginal investors, i.e. those that are on the edge of investing or not investing; these are the investors for which expected return is equal to required return, or close to equal.} I think in the notes they talk about the 'market expected return' and the 'market required return'.