Question

1. Explain the difference between the required rate of return and the expected rate of return. If they are different at a specific point in time, what does it mean?

2. What is the difference between an expected return and a total holding period return?

3. How does investing in more than one asset reduce risk through diversification?

Answer 1

(1)

• The expected rate of return is the rate an investor expects and arrives at using a probability weighted average return or otherwise.
• The expected rate of return is basically the return an investor expects after investing in an asset/ security.
• The required rate of return is the minimum rate of return an investor should receive, to make her/him invest in a security to make the invested resources worthwhile.
• The required rate of return and expected rate of return can be different.

For example:

I wish in invest in a security giving a return of at least 6% p.a. (based upon opportunity cost of other investment). After analysing past returns of ABC's share, I arrive at a return of 8% p.a.

Hence, in this case my required rate of return (minimum return) is 6% p.a.

However, by investing in ABC's share I expect to receive 8% p.a.

Thus 6% p.a. would be my required rate or return and 8% p.a. would be my expected rate of return from ABC's share.

(2)

• The holding period rate or return is the return generated by an investor from a security for the period held.
• The holding period could by for 1-year, 1-month, 1 week or even 1 day.

For example:

Miss A bought 1 share of ABC company's stock on 1st November 2018 at a price of $27.

After 1 year, on 1st November 2019 the stock's price went up to $41.

Thus, the holding period return (1-year) = ($41-$37)/$37

Holding period return (1-year) = 10.81%

On the other hand, the expected rate of return for ABC's same share would be different for Miss Annie. With her proves expectations, the expected rate of return would have been 8% p.a.

(3)

• Every asset that an investor invests into has an expected rate of return and standard deviation (risk) attached to it.
• When multiple assets are collated into one portfolio, it has an impact on the asset's expected return and expected stand deviation.
• However, the risk attached to these assets vary with respect to the correlation between them.

As we know, the standard deviation of a portfolio can be calculated as follows:

Thus, a positive correlation between assets would lead to higher standard deviation (higher risk)

At the same time, a negative correlation between the assets would reduce the portfolio standard deviation (lower risk).

Intuitively, this makes sense too. If funds are invested into assets that have a high correlation (move up/down together) then the risk would be higher. Also, if funds are invested into assets that have a low correlation (if one moves up, the other moves down) then the risk would be relatively lower.

Thus, we can conclude that investing in more than one asset reduces risk through diversification (only if the correlation between assets are negative/ low).