Question

(Related to Checkpoint 8.1) (Expected rate of return) James Fromholtz is considering whether to invest in a newly formed investment fund. The fund's investment objective is to acquire home mortgage securities at what it hopes will be bargain prices. The fund sponsor has suggested to James that the fund's performance will hinge on how the national economy performs in the coming year. Specifically, he suggested the following possible outcomes: a. Based on these potential outcomes, what is your estimate of the expected rate of return from this investment opportunity? b. Would you be interested in making such an investment? Note that you lose all your money in one year if the economy collapses into the worst state or you double your money if the economy enters into a rapid expansion. a. The expected rate of return from this investment opportunity is i Data Table State of Economy Probability Fund Returns Rapid expansion and recovery Modest growth 15% 100% 40% 30% 15% Continued recession 30% Falls into depression 15% - 100%

Answer 1

Values given:

State of Economy	Probability	Return
Rapid expansion and recovery	15%	100%
Modest growth	40%	30%
Continue recession	30%	15%
Falls into depression	15%	-100%

Formula for expected return is;

Expected Return on a security = R₁ X P₁ + R₂ X P₂ + ...... + R_n X P_n

where,

R = Return of the security under various scenarios;
P = Probability of the given scenarios

Given the values, expected return is calculated as:

Expected Return = (0.15 * 100%) + (0.40 * 30%) + (0.30 * 15%) + (0.15 * -100%) = 15 + 12 + 4.50 + (-15) = 16.50

Expected return = 16.50%

In order to understand if the security is worth investing, the risk (standard deviation) needs to be analysed. Standard Deviation is a measure of risk or volatility of a security's return. The more the volatility, higher the standard deviation.

Steps to calculate SD:
1 - Calculate (Return - Average Return) for each scenario
2 - Calculate the square of the value in step 1
3 - Multiple the value in step 2 with probability of each scenario
4 - Total of all the values in step 3 is variance
5 - Square root of variance is Standard deviation

Below table shows the calculation of each values, variance and standard deviation.

State of Economy	Return %	Probability	Return - Avg return	(Return- Avg return)2	(Return- Avg return)2 X Prob
Rapid expansion and recovery	100	0.15	83.50	6,972.25	1,045.84
Modest growth	30	0.40	13.50	182.25	72.90
Continue recession	15	0.30	-1.50	2.25	0.68
Falls into depression	-100	0.15	-116.50	13,572.25	2,035.84
					3,422.08

Avg Return	16.50 %
Variance	3155.25
Std Dev	56.17 %

As we can see, Standard Deviation is very high for this and it is a very risky investment.

Investing in asset will require further analysis as there are many factors that can affect the decision such as;
1) Risk tolerance of investor. Investors with high risk tolerance invest in riskier assets and investors with low risk tolerance invest in lower risk assets.
2) Portfolio of assets and the correlation of the current investment with the new investment. If the current portfolio of asset has zero or negative correlation with the new investment, that might help investor with diversification. When economy is collapsing, this investment may perform poorly but there might be other stocks in portfolio which may perform better (ex. non cyclical stocks).