3 - Investment risk and return

Question 1

compounding vs discounting

Answer 1

compounding = converts present val to future val
discounting = converts future val to present val

Question 2

FV formula

Answer 2

FV = PV x (1 + r)^n

r = interest rate per period
m = no. of time periods

Question 3

compounding factor formula

Answer 3

CF = (1 + (r/j))^nj

r = annual rate
n= no of years
j= number of compounding periods/year

Question 4

present val of money

Answer 4

PV = FV / (1+r)^n

n = interest/disocunt rate
n = no. of time periods

Question 5

PV of an annuity

Answer 5

annuity = series of multiple identical payments
if small no. of payments - can discount back each cash flow using PV= FV / (1+r)^n

PV annuity = £X * 1/r [1 - (1/(1+r)^n)]

£X = annuity payment paid @ year end
r =interest rate (normally annual) over the life of the annuity
n= no. of periods (normally years) that the annuity will run for

Question 6

present val of a perpetuity

Answer 6

perpetuity = series of payments paid indefinitely

PV = perpetuity payment / interest rate

Question 7

nominal vs real returns
Approx and actual calc

post tax?

Answer 7

nominal = rate of return unadjusted for inflation

approximation!
real return =nominal return - inflation rate

actual calc
(1+ nominal)/(1+ inflation) = 1 + real

post tax =
1 + post tax nom
1 + post tax real

Question 8

types of risk

Answer 8

capital risk - fall in price of cap invested or return less than expected
income risk - decreased divis
currency risk - can hedge against using forward FX rates, currency depreciating against investor
inflation risk - eroding capital
interets rate risk - duration
issuer risk - defaulting
counterparty risk - trading
ESG risk

Question 9

Total risk

Answer 9

= variance in return
= systematic risk + specific risk

specific risk can be removed through diversification (asset, geography, sector, currency, maturity)

systematic risk = market risk = beta
cannot be diversified away
economic, political, global events
liquidity, inflation, currency

Question 10

beta

Answer 10

measure of stocks volatiity in relation to overall market
B <1 = less reactive than market
B=1 - moves in line with market
B>1 - more reactive than market

Question 11

diversification

Answer 11

combination of secs not perfectly positively correlated
improves risk return trade off

Question 12

SD and variance

Answer 12

variance = SD^2

modern portfolio theory uses SD as a measure of total risk (avg deviation of returns from mean return)
assumes upside and downside SD are equally favourable - can therefore us SD up and SD down

variance = measure of volatility

Question 13

Risk measurements (4)

Answer 13

SD = volatility, variability and degree of uncertainty
- measures total risk (systematic and specific)

coefficient of variation (CV) - measure of risk vs return
CV = % SD / % avg return
= risk / return

-1<correlation<1
shows linear relation of way assets move i n relation to eachother both strength and direction

covariance - describes way asssets move in relation to eachother only directional not strength

Question 14

holding period return

Answer 14

Holding period return = return earned over period investment wad held

= [income +(end val - initial val)] / initial val

Question 15

MWRR - money weighted rate of return

Answer 15

used for PE - AKA IRR (internal RR)
used to measure performance of fund that’s had deposits and withdrawals, can be distorted by timing and size of cash flow so only relevant where fund controls this ie PE

Question 16

TWRR - time weighted rate of return

Answer 16

TWRR - for funds
removes impact of cash flows on return calc, breaks return period into sub periods
preferred over MWRR

Question 17

HPR - holding period return

Answer 17

baso % change

HPR = (val@end - val@start + income)/val@start

Question 18

TWRR (for investor)

Answer 18

removes MWRR cash flow distortion by breaking up investment period into sub periods at each cash flow

TWRR = EV1/SV1 * EV2/SV2 * EVn/SVn -1
EV = end val
SV = start val

Question 19

sharpe ratio

Answer 19

baso : excess return comparved to gov bond/total risk
calc of risk adjusted return
uses total risk - assumes no diversification
higher = greater risk adj return - better

sharpe ratio = (portfolio return - risk free return)/ portfolio stnd dev

risk free = gov bond
stnd dev = total risk

Question 20

treynor ratio

Answer 20

excess return compared to gov bond/market risk

(portfolio return - risk free)/beta of portfolio

type of risk adjusted return
systematic risk only, assumes diversification
higher = better

Question 21

information ratio

Answer 21

type of risk adj return for active funds

baso avg alpha/SD of alpha

= (portfolio return - benchmark return) / stnd dev of excess return

higher = better

Question 22

efficient market hypothesis EMH

Answer 22

attempts to explain efficiency =info about firms.
/shares freely available and correctly interpreted and included in price

weak form - stocks can be mispriced. market price reflects historic share prices, behavioral contributions and not all info accessible (would use active strat)

semi strong - market price reflects historic share prices and all publicly available info

strong - shares generally not misprices
market price reflects historic prices, all publicly avail info and all private info (would use passive strat)

Question 23

assumptions and shortcomings of EMH

Answer 23

assumes that because info exists aout shares - it will have been used by investors making decisions

• just because info is there people may not use it (correctly)
  -large instit investors have their own laborious processes
• not everyone able to correctly analyse info
• not everyone acts independently of eachother

Question 24

capital asset pricing model (CAPM)
assumptions?

Answer 24

calculates expected return from a sec given it’s systematic risk

E(Rp) = Rf + (Rm - Rf)Bp
expected ret for stock P = risk free return + (excess return on market)*B of stock P

CAPM flawed unless all assumptions are true
- everyone can borrow and lend @risk free rate (no)
- everyone well diversified so no spec risk (no)
- no tax or transaction costs (no)
-all investors want to maximize ret and minimize risk (yes)
- all have same expectations (relies on strong EMH)

Question 25

Jenson measure

Answer 25

compares funds actual return with CAPM expected return

Jensens alpha = Rtn (portfolio) - Rtn (CAPM)

Question 26

arbitrage pricing theory (APT) vs CAPM

Answer 26

CAPM = single factor model (beta), more restrictive assumptions than APT

APT - multi factor (more than just beta) e.g. inflation, industrial production, credit spreads

adv - more accurate than CAPM because more variables, fewer assumptions

dis - factors may be correlated and may change

Question 27

Multi factor return models

Answer 27

tries to identify main factors that explain a funds return
3 cats of model:
macro - inflation, interest, unemployment
fundamentals - earnings, divi, yield
statistical - e.g measuring stock market indices

Question 28

r squared

Answer 28

measure of market risk - indicates correlation of portfolio return to benchmark return
shows explanatory power of a model - from 0-100

Question 29

types of investor bias (5)

Answer 29

Loss aversion - tendency to strongly prefer avoiding losses to making gains - accept more risk to avoid loss than make gains

risk aversion - accept smaller more certain gains

Confirmation bias – looking for information to support our belief

Hindsight bias – making (potentially) erroneous links between past events

Cognitive bias – incorrect judgement based upon our way of thinking

Question 30

4 theories of behavioural finance

Answer 30

Prospect theory
Responding differently to the same situ depending presentation as loss or gain

Regret theory
Avoiding the admission of a bad choice, e.g.
Not selling loss-making positions,

Anchoring
Basing decisions on recent data and avoiding long-term trends

Over and under-reaction
Becoming optimistic when markets rise and pessimistic when markets fall

Question 31

synthetic risk and reward indicators

Answer 31

SRRI - included in KID
required by UCITS and PRIIP

risk reward measure, 1-7 score of volatility of returns (measured using NAV) over 5 years
lower score = lower risk(/reward)

Question 32

FV of an annuity

Answer 32

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