3 - Investment risk and return Flashcards
compounding vs discounting
compounding = converts present val to future val
discounting = converts future val to present val
FV formula
FV = PV x (1 + r)^n
r = interest rate per period
m = no. of time periods
compounding factor formula
CF = (1 + (r/j))^nj
r = annual rate
n= no of years
j= number of compounding periods/year
present val of money
PV = FV / (1+r)^n
n = interest/disocunt rate
n = no. of time periods
PV of an annuity
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
present val of a perpetuity
perpetuity = series of payments paid indefinitely
PV = perpetuity payment / interest rate
nominal vs real returns
Approx and actual calc
post tax?
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
types of risk
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
Total risk
= 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
beta
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
diversification
combination of secs not perfectly positively correlated
improves risk return trade off
SD and variance
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
Risk measurements (4)
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
holding period return
Holding period return = return earned over period investment wad held
= [income +(end val - initial val)] / initial val
MWRR - money weighted rate of return
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
TWRR - time weighted rate of return
TWRR - for funds
removes impact of cash flows on return calc, breaks return period into sub periods
preferred over MWRR
HPR - holding period return
baso % change
HPR = (val@end - val@start + income)/val@start
TWRR (for investor)
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
sharpe ratio
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
treynor ratio
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
information ratio
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
efficient market hypothesis EMH
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)
assumptions and shortcomings of EMH
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
capital asset pricing model (CAPM)
assumptions?
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)
