Risk and return (w2)

Question 1

What is the difference between nominal and real interest rate?

Answer 1

Nominal = growth rate of money
Real = growth rate of purchising power

Question 2

How is real interest rate (rr) calculated?

Answer 2

Real interest rate = (rn - i) / (1 + i)

Question 3

What is the Fisher Equation?

Answer 3

rr = rn + E(i)

Denotes the relationship between demanded nominal rates and inflation

As expected inflation E(i) increases, so does the expectation for the nominal rate (rn) to minimise the decrease in real rate (rr)

To ensure the value of money does not decrease overall

Question 4

How to calculate a risk free rate of return on a zero coupon bond?

Answer 4

Risk free return at time t=1
rf = face value / price at maturity -1

rf = fv / P(t) - 1

Face value = par value –> price received at maturity

Question 5

How is holding period return determined?

Answer 5

HPR = (Price in period t1 - Price in period t0 + Dividends in t1) / Price in period 0

HPR = (P1 - P0 + D1) / P0

Question 6

Why are long term, low-risk investment unattractive?

Answer 6

Because of the negative correlation between inflation and real interest rate, the nominal rate often does not compensate for the soaring inflation, decreasing the value of the investment

Question 7

How are expected returns of an investment calculated? Why is it important to estimate those?

Answer 7

Expected return = sum of (probability x return) for all states

E(r) = Σp(s) * r(s)

Important as when entering an investment, future return is unknown = must be estimated

Expected return = weighted mean

Question 8

You’ll need E(r)

How to calculate variance of an investment?

Answer 8

Var = sum of [probability * (return in state - expected return) ]

Var = Σ p(s) * [ r(s) - E(r) ]^2

Note: return for each state is adjusted by the expected return to track deviation around the mean

Note: because it is a variance, r(s) - E(r) is SQUARED to ensure all values are positive

Risk = deviation around the mean

Question 9

How to calculate variance when probabilities are unknown? How to convert it into SD?

Answer 9

VAR = 1/n * Σ r(s)

SD = sqrt of var

note: for SD, n becomes n-1

SD = sqrt of final VAR equation

Question 10

What is risk premium?

Answer 10

The difference between the return on a risk free asset r(f) and the risky investment

Calculated as a difference between the HPR of both

Question 11

What is Sharpe Ratio?

Answer 11

Sharpe Ratio = risk premium / SD of excess return

Note: since the risk free asset has a SD = 0, SD of excess return = SD of a risky asset

Sharpe Ratio = the slope of CAL

Question 12

How does SD measures risk?

Answer 12

SD measures volatility

Therefore, the lower the SD the safer the stock
–> If SD is present, positive SD is preferred

If SD > E(r)
–> Expected returns do not compensate for the risk
–> The returns can be expected to be negative

Question 13

How to estimate investment returns using historical data?

Since future states and their probabilities are unknown

Answer 13

Expected return = sum of historical returns / number of time periods

E(r) = 1/n * Σ r(s)

Probabilities of scenarios are replaced with historical outcomes which are observable

Question 14

Why is normal distribution of the returns important?

3 reasons

Answer 14

1. If returns follow a normal distribution, SD is an accurate measure of risk
2. If all security returns are symmetrical, so will be the return of the portfolio
   –> E(r) and SD can be used for estimating scenarios

Question 15

What are the 2 consequences of not normally distributed returns?

Answer 15

1. SD does not reflect risk accurately
2. Sharpe ratio no longer gives an accurate measure of portfolio performance

Question 16

What are the 2 reasons for negative skew in investment portfolio?

Answer 16

In terms of capitalisation: many small firms, a few giants

In terms of returns: small firms often outperform large firms (SMB)

Question 17

What 3 properties do risk averse investors look out for in an investment?

Answer 17

1. Risk free returns
2. If risk is assumed, positive risk premium is required
3. Mean variance principal

Question 18

What is the equation for utility, using risk aversion? When will the risk aversion have a positive or negative value?

Answer 18

U = E(r) - (1/2 * A * var)

Risk aversion: A > 0, the aversion offsets the return
Risk seeking: A < 0, risk adds to the return in creating utility
Risk neutral: A = 0, the utility is solely based on E(r)

Question 19

What is the mean-variance portfolio?

Answer 19

For portfolio A to dominate portfolio B

E(r) of A >= E(r) of B
SD of A <= SD of B
–> at least one must be an inequality to establish dominance

Question 20

What characterises all portfolios on the same indifference curve?

Answer 20

• They yield the same utility
• They are equal according to the mean-variance criterion

However, higher indifference curve is preferred

Question 21

How to calculate an optimal asset allocation in complete portfolio that minimises risk?

When expected returns, SD and risk aversion is given

Answer 21

y* = [ E(r) - r(f) ] / (A * Var)

Var = variance of the risky portfolio as risk free asset has a variance = 0

Derivative of r(f) + y * [E(r) - r(f) ] - [ 1/2 A * y^2 * var ]

Question 22

What is the difference between risky and complete portfolio?

Answer 22

Risky = combination of risky investments, manipulated through weights

Complete = combination of risky and risk free asset, based on risk aversion

Question 23

What is Capital Allocation Line?

Investment opportunity set

Answer 23

The graphical representation of the Sharpe Ratio
–> slope of CAL shows the marginal increase in E(r) for the unit increase of risk

Depicts all possible complete portfolios with different weights y in the risky portfolio

Question 24

What causes the change in steepness of the CAL?

Answer 24

Different lending and borrowing rates in the investment opportunity set

Question 25

How is the E(r) of the complete portfolio calculated?

Answer 25

E(r) = r(f) + y * [ E(r) - r(f)
Expected return of the complete porftolio = risk free return + risk premium adjusted by the weight of the risky portfolio in the optimal porfolio

Question 26

How is the variance of the complete porfolio estimated?

Answer 26

Variance = y^2 * SD^2
SD = y * SD

Question 27

What is a passive investment strategy? What are its advantages?

Diversification and market forced

Answer 27

Investment in a market index, which is diversified and adjusts based on supply and demand forces of the market

–> When using an active strategy, the cost of management must be considered, passive strategy gives the free rider benefit

–> Returns are comparable to those of an active investment strategy as it is difficult to outperform the market

Question 28

What is the Capital Market Line?

Answer 28

Capital Market Line = graphical depict of feasable investment options in a complete portfolio, which uses risk free asset and market index instead of the risky portfolio