Risk and Return Analysis

Question 1

RISK

Answer 1

Definition – the set of unique consequences for a given decision which can be assigned probabilities e.g 1 in 6 chance of obtaining a six from a single die.

Question 2

Types of risk

Answer 2

-Business risk-Variability in the firm’s cash flows (outflows are greater than inflows)
-Financial risk-risk associated with the use of debt
capital/loans. Higher the level of loans, the higher the level of financial risk.
-Portfolio or market risk-variability in investors returns on investment.

Question 3

Risk-free and Risky assets

Risk-Free assets

Answer 3

-Return is known with certainty
For example investing Rs100, at 5 % over 1 year, After 1
year, you receive Rs105
-Examples: Treasury Bills, Notes, bonds ( issued by the
govt)
No credit risk/ no risk of default.

Question 4

Risky assets

Answer 4

-Return is not known with certainty

-Examples: financial products such as shares
securities issued by companies

Question 5

RETURN

Answer 5

The return on an investment measures the increase or decrease in wealth through an investment
ROI = Final wealth – Initial amount divide by Initial amount invested
For example, you are investing Rs100 in a govt security that pays
Rs110 in 1 year’s time. Find the rate of return?
Rate of return = (110 – 100) / 100
= 0.1 = 10%

Question 6

Expected return on single assets

Answer 6

-It is an estimate of the return that a risky asset can provide at end of investment period.
For example, investing Rs100 today.
What can happen at the end of 1 year?
Lower amount Rs90, same amount Rs100, higher amount Rs120
This year we are in financial crisis and next also crisis will continue.
The following must be estimated:
-Future economic conditions
-Possible returns attached to the states
-Probabilities associated with different states
[R= E(R) =]
Example:
Economic condition prob (p) Possible returns(r)
Strong economy 0.15 0.2
Weak economy 0.15 -0.2
No major changes 0.70 0.1
Calculate the expected return.
(0.15 x 20) + (0.15 x -20) + (0.70 x 10) = 7%

Question 7

Measuring risk

Answer 7

Defined as the variability of actual return from
expected return
ER 7%, Act Return 15%, Risk high
Risk can be measured using:
-Variance
-Standard deviation ER 7%, Act Return 2%, Risk high

Question 8

Standard deviation

Answer 8

(slide)

Question 9

Total risk

Answer 9

-Standard deviation is a measure of total risk
Comprises 2 elements:
-Unsystematic risk/specific/avoidable/diversifiable/
idiosyncratic – variability in returns associated with factors unique to a given asset/company for example
poor management of a company.
-Systematic risk – market risk/non diversifiable/unavoidable: variability in returns associated with macro economic factors for example inflation, changes in general interests rates.
(slide)

Question 10

Comparing risky assets

Answer 10

• A relative measure must be used, the Coefficient of Variation (CV)
  -Lowest CV
  -Measures the level of risk per unit of return
  CV = Standard deviation of return divide by Expected return of asset
  Ex 1
  E(R)A = 15%, ER on B = 20%, Sd A = 4%, Sd B = 3%
  Ex 2
  E(R)A = 25%, ER on B = 20%, Sd A = 4%, Sd B = 4%
  Ex 3
  E(R)A = 20%, ER on B = 20%, Sd A = 4%, Sd B = 3%

Question 11

Risk and return - Portfolio

Answer 11

-Investor buys a group of individual financial assets
-How to choose among portfolios?
Expected return and
Standard deviation must be calculated
Portfolio theory developed by Markowitz in 1952

Question 12

Portfolio Theory

Answer 12

Some general assumptions of the theory need to
be clarified:
Optimum portfolio
-Investors want to maximise the returns from the total set of investments for a given level of risk.
-The full spectrum of investments must be considered because returns from all these investments interact and this relationship among the returns for assets in the portfolio is important.
(ii)Risk Aversion
-Portfolio theory assumes that investors are basically risk-averse.
-Most investors committing large sums of money to developing an investment portfolio are risk averse.
-Therefore, we expect a positive relationship between expected return and expected risk.
(iii) Risk

Question 13

Markowitz Portfolio Theory

Answer 13

-In the early 1960s, the investment community talked
about risk, but there was no specific measure for the
term.
-The basic portfolio model was developed by Henry
Markowitz (1952,1959) who derived the expected rate of return for a portfolio of assets and an expected risk measure.
-Markowitz showed that the variance of the rate of
return was a meaningful measure of portfolio risk under a reasonable set of assumptions and he derived the formula for computing the variance of a portfolio.

Question 14

Expected return on Portfolios

Answer 14

An estimation of the return that may be obtained from a portfolio
Expected return E( ) comprising 2 assets, A and B, will be: (slide)

Question 15

Covariance

Answer 15

Covariance between rate of return of 2 assets measures in which direction returns on the assets are moving
Types of covariance:
-Positive covariance
-Negative covariance
-Zero covariance

Question 16

Covariance Formula

Answer 16

(slide)

Question 17

Correlation coefficient

Answer 17

Direction in which returns are moving estimated through covariance.
However, degree to which returns are moving together or in opposite directions is measured through correlation coefficient.
Measures the degree of relationship between the returns of 2 individual assets.
formula: (slide)

Question 18

Portfolio risk

Answer 18

It is given by standard deviation of the portfolio
Calculated by considering standard deviation and correlation coefficient between returns on individual assets.
Formula: (slide)