3 - Principles of Investment Risk and Return (9/80)

Question 1

Future Value

Answer 1

FV = PV x (1 + r) ^ n
= PV x (1 + r/j) ^ nj

j = compounding intervals per year

Question 2

FV of Annuity

Answer 2

‘Annuity due’ - paying in extra at start of the year

FV = Payment x [ ( (1+r)^n - 1) / r ] x (1+r)

‘Ordinary annuity’ - paying in extra at end of the year (so interest doesn’t apply to deposit)

FV = Payment x [ ( (1+r)^n - 1) / r ]

Question 3

Systematic vs Non-Systematic Risk

Answer 3

Systematic = whole of market risks (can’t be diversified)

Non-systematic = industry/business specific (can be diversified)

Question 4

Holding Period Return

Answer 4

HPR = [Price at End - Price at Start + Income] / Price at Start

Question 5

Money-Weighted Rate of Return (MWRR)

Answer 5

Measures overall returns, taking into account cash inflows and redemptions

V1 = V0(1 + r) + CF(1 + r) ^ Wk

V0 element is the original FV calc if no cash flows
V1 is the final capital

Wk = (TD - Dk) / TD

TD = Total days in period (e.g. 31)
Dk = days elapsed since start

Run a few times to estimate r

Question 6

Time-Weighted Rate of Return (TWRR)

Answer 6

Split returns into different periods and combine them

E.g. Rate 1 = (End Value / Start Value) - 1

TWRR = [ (1 + R1) * (1 + R2) ] - 1

Question 7

Variance and Standard Deviation

Answer 7

Variance = S.D ^ 2 = [ (return1 - mean return)^2 + (return2 - mean return)^2…. ] / N

2/3rds chance of returns falling within one standard deviation of the mean
E.g. mean return = 5%, s.d. = 2%
= 2/3rd chance of being 3% - 7%

Coefficient of Variation = S.D / Mean Return

Question 8

Sharpe Ratio

Answer 8

(Rp - Rf) / S.D.

Question 9

Treynor Ratio

Answer 9

(Rp - Rf) / Beta

Assumes all market risk is diversified away
Performance of undiversified funds will be overstated

Question 10

Jensen Measure (ALPHA)

Answer 10

Rp - Rcam

Rcam = R predicted by CAPM

Rp = Rcam => on the Security Market Line
Rp > Rcam = above the SML
Rp < Rcam = below the SML (not worth investing in)

Question 11

Information Ratio

Answer 11

(Mean of Excess Returns) / (S.D. of Excess Returns)

Measures skill of active managers

Question 12

Portfolio Holding Period Return

Answer 12

Rp = (Wa x Ra) + (Wb x Ra)

Weighted average of returns

Question 13

Portfolio Standard Deviation

Answer 13

Question 14

Efficient Market Hypothesis

Answer 14

Information is freely available so is priced in

Weak form = all historic info
Semi-strong = all public info
Strong = all insider info

Question 15

Modern Portfolio Theory

Answer 15

1. Investors demand more return for more risk

2. Lower correlation reduces portfolio risk

Question 16

Efficient Frontier

Answer 16

Moving up too much doesn’t give as much return for risk taken -> diminishing margin of gainz

Question 17

Arbitrage Pricing Theory

Answer 17

Multi-factor Beta
More accurate than CAPM with fewer assumptions

Relies on factors being uncorrelated

Question 18

Types of Multi-Factor Model

Answer 18

Macroeconomic
Fundamental
Statistical

Question 19

Behavioural Biases

Answer 19

Loss aversion
Confirmation bias
Hindsight bias
Cognitive bias

Question 20

Behavioural Theories

Answer 20

Prospect (placing more value on perceived/potential gains)
Regret (avoid trading out of regret)
Anchoring (recent news favoured most)

Question 21

Present Value

Answer 21

PV = FV / [ (1 + r) ^ n ]

Annuities = CF x [ (1 / r) - (1 / r(1+r)^n) ]
or use discount factors one after the other and sum:
Year 1 = (1 + r) ^ 1
Year 2 = (1 + r) ^ 2 etc.