Risk and Return

Risk includes the possibility of losing some or all of the original investment. 

Types of risk:

Business risk
Financial risk
Portfolio or market risk

The Return on investment measures the increase or decrease in wealth through an investment.


Expected return on single assets
It is an estimate of the return that a risky asset can provide at end of investment.

Variance




E(R) = (0.15 X 0.2) + (0.15 X -0.2) + (0.7 X 0.1) =  0.07 OR 7%

Variance= [0.15 X (0.2 - 0.07)²] + [0.15 X (-0.2 - 0.07)²] + [0.7 X (0.1 - 0.07)²] = 0.0141
Standard deviation = 0.119 OR 11.9%

Unsystematic risk
Unsystematic risk, also known as "specific risk," "diversifiable risk" or "residual risk," is the type of uncertainty that comes with the company or industry you invest in.
e.g. ineffective management of the company

Systematic risk
In finance and economics, systematic risk is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income.

Coefficient of variation
It measures the level of risk per unit of return.

Lowest CV = Lowest level of risk per unit of return

Portfolio (risk and return)

Assumptions of the Markowitz Portfolio Theory

1. Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period.
2. Investors maximize one-period expected utility and their utility curves demonstrate diminishing marginal utility of wealth.
3. Investors estimate risk on basis of variability of expected returns.
4. Investors base decisions solely on expected return and risk.
5. Investors prefer higher returns to lower risk and lower risk for the same level of return.

Formula:
E(Rp) = αA[E(RA) + αB[E(RB)] ◘◘◘ α ≈ Stock weight

Positive E(Rp) = Return from both assets move in the same direction. (A↑ B ↑ , A↓ B↓)

Negative E(Rp) = Return from both assets move in opposite direction. (A↑ B↓ . A ↓ B↑)

Zero E(Rp) = Return from both assets are independent.

Co-variance of portfolio

Co-variance between rate of return of 2 assets measures in which direction returns on the assets are moving.

Type of co-variance: Positive, negative and zero

All investors will prefer a negative co-variance

Formula:

Co-variance of portfolio

Correlation coefficient
It means the direction in which returns are moving estimated through covariance

Correlation coefficient

Value Range from -1 to +1
e.g. -0.8 → Strong negative association between return on A and return on B.

Portfolio risk

Risk

Minimum Risk portfolio with 2 assets

Question and Answer

Q1:

Gerrybuild Plc is a firm of house builders. It is considering 2 design types, small houses and large houses. The following information is available:

Required: (a) Find the expected return and risk from large houses and small houses.

(b) Find the covariance between large and small houses, and hence determine the degree of association between them.

                (c) Determine the minimum risk portfolio.

                (d) Find the expected return and risk under the minimum risk portfolio.
a)
E(RA) = 3000
E(RB) = 2400

(b)


(c)


(d)


Q.2:
The expected return on a bond fund is 5.4% and 9.4% on a stock fund. The respective standard deviations are 3.7% and 6.1%. The correlation coefficient is 0.9. What is the standard deviation of this portfolio if you invest the same amount of money in each fund?


Q.3:

Hill’s Financial Services gathers earnings forecasts and analyzes them for its subscribers. Ten analysts forecast Ford Motor Company’s earnings per share next year. Three analysts predict $5.75, two analysts forecast $5.90, one analyst predicts $6.25, and four analysts forecast $6.30. For simplicity, assume these forecasts are the only possible outcomes and the analysts are equally likely to be correct. In decimal form, what is the variance for Ford’s EPS given the above forecasts?

Q.4:

The expected return on a bond fund is 5.4% and 9.4% on a conservative stock fund. The respective standard deviations are 3.7% and 16.1%. The covariance is 20.24%². What is the correlation coefficient?

ANS: Correlation coefficient = 20.24/(3.7*16.1) = 0.34

Q.5 

You are considering investing equally in two assets. Asset A is a Blue Chip stock and Asset B is a Growth stock. What would be the covariance of a portfolio for these two stock given the below information?

State of the Economy	Probability of Occurrence	Return on Asset A	Return on Asset B
Poor	0.1	−3.0%	2.0%
Stable	0.3	3.0%	4.0%
Good	0.4	7.0%	10.0%
Excellent	0.2	10.0%	20.0%

E(RA) = (0.1*-3) + (0.3*3) + (0.4*7) + (0.2*10) = 5.4
E(RB) = 9.4


Q.6:

The expected return on a government money market fund is 3.4% and 9.4% on a growth stock fund. The respective standard deviations are 0% and 30%. The correlation coefficient is 0.10. What is the standard deviation of this portfolio if you invest the same amount of money in each fund?