Question

a) Discuss the benefit of portfolio diversification. Explain how to achieve diversification benefit. An investor buys 1 share of ABC Ltd at the price of $32 on December 1, 2019. The firm is not expected to pay any dividends. Consider the following three possible scenarios for the share price on December 1, 2020: $50 with a probability of 20% $35 with a probability of 65% $23 with a probability of 15% b) Calculate the expected return for holding the share for a year. c) Calculate the variance of return and standard deviation of return.  d) On December 1, 2020, the share is worth $38 and the investor just received a dividend of $3. Calculate the total holding period return and capital gains return over the one-year period. e) Explain the difference between expected return and realised return.

Please show working on a piece of paper

Answer 1

A. Discuss the benefit of portfolio diversification. Explain how to achieve diversification benefit,

.

Diversification refers to holding a wild range of investment in a portfolio.

*The primary benefits of diversification is to reduce the variability or risk of a portfolio

*Diversification reduce portfolio risk as long as different investment are unlikely to move in the same direction, meaning they are not perfectly positively correlated.

*A diversified portfolio minimizes the overall risk associated with the portfolio.

*Generating returns – sometimes investments don’t always perform as expected, by diversifying you’re not merely relying upon one source for income, here we get continues income.

.

An investor buys 1 share of ABC Ltd at the price of $32 on December 1, 2019. The firm is not expected to pay any dividends. Consider the following three possible scenarios for the share price on December 1, 2020: $50 with a probability of 20% $35 with a probability of 65% $23 with a probability of 15%

B. Calculate the expected return for holding the share for a year

Share price on Dec 1, 2020	Return	Probability	Expected return
$50	(50 - 32)/32 = 0.5625	20%	0.1125
$35	(35 - 32 )/32 = 0.09375	65%	0.0609
$23	(23 - 32)/32 = -0.2813	15%	-0.0422
.	.	Total	0.1312

Expected return = 0.1312 = 13.12%

.

C. Calculate the variance of return and standard deviation of return.

Share price on Dec 1, 2020	Return (R )	Probability(P)	Expected return (RP)	(ER - R)	(ER - R)^2
$50	(50 - 32)/32 = 0.5625	20%	0.1125	-0.4313	0.1860
$35	(35 - 32 )/32 = 0.09375	65%	0.0609	0.0703	0.0049421
$23	(23 - 32)/32 = -0.2813	15%	-0.0422	0.1734	0.030067
.	.	Total	0.1312

Expected return (ER) = 0.1312

Share price on Dec 1, 2020	Probability(P)	(ER - R)^2	(ER - R)^2 *(P)
$50	20%	0.1860	0.037203938
$35	65%	0.0049421	0.003212358
$23	15%	0.030067	0.004510134
.		Total	0.04492643

SD (standard deviation) = root off sum (ER - R)^2 *(P)

Variance = SD^2

So,

Variance = 0.04492643

SD = root off 0.04492643 = 0.2119 = 21.19%

.

D. On December 1, 2020, the share is worth $38 and the investor just received a dividend of $3. Calculate the total holding period return and capital gains return over the one-year period.

.

Holding period return(HPR) = ( Capital gain + dividend ) / Past price

Where,

Capital gain = Present price - past price = ( 38 - 32 = 6

Dividend = 3

Past price = 32

,

HPE = ( 6 + 3 ) / 32

HPE = 9 / 32 = 0.2813 = 28.13%

.

E. Explain the difference between expected return and realized return.

.

Expected return means the return investors expect to realize if an investment is made. The expectation is truly based on the return of a risk free investment, plus a risk premium. In case of a higher risk, a higher return is expected to compensate for the increased risk and vise verse.
.
Realized return is the return actually earned by buying an securities. In other word actual return on an investment for some previous period of time is called realized return. Realized returns are not connected to expected returns.