9. PORTFOLIO PERF Flashcards
Holding period return
Doesnt take CF timing into account
non risk adjusted
Money weighted return
Non risk adjusted
Adjusts for inflows and outflows
Skewed by timing and size of CFs
Time weighted return
non risk adjusted
takes timing of CFs into account
most fair appraisal of perf
IRR
take 2 discount rates - 1 low and 1 high
n1 = npv with r1
n2 = npv with r2
MWRR vs TWRR
MWRR
- strongly influenced by timing and size of CFs which may be accidental or contigent to performance
- good if FM is in control of these
- basically IRR of opening and closing values of portfolio taking into account inflows an outflows via interpolation
avg growth rate of invested money
TWRR
- generally preferable as not influenced by timing and size of CFs
- geometric growth rate - calc returns between CFs then combine line compound interest
Should produce similar results in normal conditions
- dissimilarities occur when CFs are large relative to portfolio
- MWRR will be higher if more £ invested @ earlier periods
Benchmark properties
S specified in adv and not changing to suit perf
A appropriate to preferences of fund (region/size/style etc
M measurable and calculateable frequently
U unambiguous w/ clearly defined weights
R regularly reported
A appropriate to currency
I investable and owned
Types of investment objective
Target income replacement
- e.g. salary/retiree
- or target for annuity purchase
Liability/lump sum driven
- allocates resources to meet specific liability in future
Best efforts
- maximizing returns for given risk without setting target returns
- reduces risk of not meeting targer but client may fall short of goals later in life
Benchmark driven
- bench +/- relative to inflation/GDP/global benchmark etc
Implications of ESG restrictions on benchmark selection
regular benchmarks dont capture non financial performance of ESG constrained funds
- global impact funds often have ACWI benchmarks
- FTSE4GOOD contains shell - investors with oil and gas restrictions will likely see big divergences due to this
Myner’s review
2001 Myners review - looked at weakness of peer benchmark approach for pension fund managers
- recommended a customised benchmarking approach where fund considers
- suitability of index benchmarks in achieving fund objectives
- whether active or passive management appropriate for each asset class
where active = appropriate
-set divergence limit for managers to operate within
encourage active management to be undertaken with conviction
Peer group benchmarks
Can encourage herding mentality and managers wanting to avoid being the worst of a bunch (even if entire group is bad)
widely accepted practise still but problematic because
- too broad a group often
- not specified in advane or investable
- survivorship bias
types of benchmark
Peer group
broad market
factor/style based
custom benchmark
OR
relative/absolute return
best effortsq
TOTAL CONTRIBUTION
= sum ( Wp x Rp - Wb x Rb)
Wp = weight in portfolio
Rp = return portfolio
Wb = weight benchmark
Rb = return in benchmark
sum of all sectors/assets
CONTRIBUTION FROM AA
= SUM (Wp - Wb) Rb
= SUM(WpRb) - SUM(WbRb)
Wp -Wb = benchmark overweight/underweight
Wp = weight in portfolio
Wb = weight benchmark
Rb = return in benchmark
SUM all secotrs/assets
CONTRIBUTION FROM STOCK SELECTION
= SUM (Rp - Rb)Wp
(Rp- Rb) = excess return over benchmark
Jensen’s alpha
Jensen’s alpha = actual return - CAPM predicted return
CAPM = Rfr + B (Rm - rfr)
RELATIVE DURATION
basically CAPM with duration instead of B
Rp = Rf + [ Dp / Dm(Rm - Rf) ]
SHARPE RATIO
XS returns over RFR per unit of risk
compares total risk in terms of stnd dev with returns
stnd dev = non diversified portfolios
- assumes normal distro which may not always be the case (leptokurtosys)
Traynor uses B - useful for diversified portfolios where specific risk has been diversified away
Problems
- stnd dev includes both neg and positive variances from the mean
- Sortino solves this as uses only semivariances (negative/bas deviations from mean)
SORTINO RATIO
XS return per unit of risk but downside risk only
removes good/positive variances from stnd deviations
stnd dev of svp = stnd dev of semi variances = deviations below mean
still SD so still for non diversified portfolios
when calc SD of svp = still divide by big N (e.g. if 40 -ve variances and 60 +, still sum and square the 40 then divide by 60)
ALTERNATIVE SORTINO RATIO
using XS returns over target reate
still SD of svp
when client is v sensitive to loss - return of target = 0
TREYNOR MEASURE
numerator = XS returns over rfr
denominator = beta = diversified portfolio
XS return per unit of systematic risk
Cost/benefit of risk/return trade off - assumes unsystematic risk is diversified away
INFORMATION RATIO
more generalized form of sharpe where benchmark isnt rfr
often used to gauge manager skill
Gauge of investment value added
measures xs return of fund vs benchmark divided by degrees of freedom (TE) fund takes relative to BM
M2 RATIO
Client friendly version of Sharpe - saying ‘if we took the same risk as he benchmark’
if you ranked funds according to Sharpe and M2 the lists would be the same
R^2
= correlation coefficient^2
= explained variance
correlation coeff = 0.8
R^2 = 0.8 x 0.8 = 0.64
SO 64% of co movement between 2 variables is explained by linear equation
SO unexplained variance = 1-R^2 = 36%
VaR
M£ = £ invested in portfolio
oP = portfolio risk in SD terms
Za = Z score = standardised variable/Tstat
Conditional VAR = expected loss once market moves beyond normal limits
VAR describes just 1 point in tail of distribution
CVAR more comprehensive measure of that part of the tail risk - considers probability weighted loss in the alpha part of the normal distribution tail
AKA tail VAR
if u assume normally distributed returns CVaR can be estimated using means and SD
Active share
Sum differences in weightings of each sec (benchmark vs portfolio)
divide by 2
VaR
Value at risk (VaR) quantifies potential financial risk for an investment or a portfolio, by offering a quantitative estimate of the maximum probable downside over a specified time horizon.
VAR = Expected return - (portfolio vol x t-stat for the confidence level)
How to work out VAR confidence levels
t stat = no. of SDs from mean
% values = % of values within that no. of SDs
only concerned with neg tail SO 95% of values = (100-95)/2 + 95 = 97.5% confidence level
(2.5% negative tail)
Annualised risk/SD
Tells us high tightly investment returns are clustered around mean
Most used metric for measure of variability
Drawdown
Calc drop from highest peal val to lowest trough val in period - reports as % change
DD = Price (min) / Price (max) -1
Avoiding large DD is important for
- risk averse investors
-those drawing an income from a fund -
- cystallising lump sums
