Week 3 - Portfolio Theory & CAPM

Question 1

RISK
Finding the Standard variance of returns

Answer 1

Risk can be measured as the standard deviation of returns

Work out the average return based on likely outcomes. For each likely outcome, subtract the mean and square the result

Work out the average of those squared differences to get the variance. The
denominator can be N or N-1 depending on if it is a sample or the whole
population. Your book says use N-1 for the past and N for the future. The

Excel formula is either VAR or VARP where P stands for population

Take the square root of variance to get the standard deviation. The Excel formulae are either STDEV or STDEVP

Question 2

Expected Returns
Two Projects, A&B
Two economic states, boom & recession. Both equally likely to happen
Boom: A 70% Return, B 10%
Recession: A -20%, B 30%

Find expected returns

Answer 2

Project A:
Boom: Probability 0.5, Return 70%
0.5x70% = 0.35
Recession: 0.5, Return -20%
0.5 x -20% = -0.1
Expected Return = 0.35 + -0.1 = 0.25

Same for project B

Question 3

Calculating variance of Expected Returns & Standard deviation

Answer 3

Subtract the return from the expected return e.g. (Example from earlier flashcard with 70% or -20% return, 0.25 ER)

0.7 - 0.25 = 0.45 Deviation from ER
-0.2 - 0.25 = -0.45 Deviation

Square the Deviation
0.2025 & 0.2025

Multiply the Squared deviation by the probability i.e.
0.2025 x 0.5 = 0.10125
Add together for both probabilities (0.10125 + 0.10125)

= 0.2025 VARIANCE

Square root of the variance is the Std.D
= 0.45

Question 4

Portfolio Expected Return

Answer 4

Portfolio weight of asset x ER of asset… cont.
e.g.

W1 x ER1 + W2 x ER2 + W3 x ER3 etc.

Question 5

Finding the risk of a 2-Asset Portfolio
IMPORTANT
(2 is the max you will be asked for)

Answer 5

Must find the COVARIANCE
=Sum: prob. [Ra - ERa] [Rb - ERb]

Prob. = 0.5 (continuation of previous example)
Ra = 0.7
ERa = 0.25
rA - erA = 0.45

Rb = 0.1
ERb = 0.2
rB - erB = -0.1

(rA - erA) x (rB - erB) = -0.045
-0.045 x Prob. (0.5) = -0.0225

Repeat for the recession outcome and add the two together gives:
-0.0225 + -0.0225 = -0.045 COVARIANCE

Question 6

Finding correlation coefficient of the two projects

Answer 6

Cov(A,B/Std.D(A)*Std.D(B)

= -0.045/0.45*0.1
= -1
Perfectly negatively correlated

Risk reduces as correlation goes from +1 to -1

Question 7

Beta & beta values

Answer 7

Sensitivity of the asset to market changes.
Beta is the only risk measure required by a fully diversified
investor

<0 - Opposite direction to the market index
=1 same direction and movement as the market
0 - uncorrelated with market
>1 - Same direction but greater than the movement of the market

Question 8

Capital Asset Pricing Model CAPM Assumptions

Answer 8

Investors hold diversified portfolios

Investors are rational and risk-averse

Investors are price-takers

Investors can borrow and lend unlimited amounts at
the risk-free rate of return

No transaction or taxation costs

No information asymmetry

Question 9

CAPM Limitations

Answer 9

Unrealistic assumptions:
- Many investors are not well diversified
- Perfect capital market assumptions are unrealistic

Beta is calculated using historical data without considering what is likely to happen in the future

Market evidence exists that cannot be explained by the
CAPM ( small firms are riskier, ‘value’ firms have higher
returns, firms with ‘momentum’ do better etc)