Chapter 8 Portfolio Performance Flashcards
Median
Mean
Median:
The return that other returns have a 50% chance PPF being above and a 50% chance of being below
- Put returns in order
- if it is an odd number of returns, it is middle figure
- if it is even number of returns, it is the mean of the middle two returns
Mean: - Average of returns ,each return weighted by probability of it happening Multiply each return by their probability, then total the resulting weighted probability Example: Share price over last 5 days: 130,136,132,138,136 Median would be - 130 ,132,136,136,138. = 136
Mean
130+132+136+136+138
———————————- = 672. = 134.4
5. 5. .
Weighted Probability Example:
(-) 5% 0% 5% 10%
2 2 4 2
One Year Return PROBABILITY RXP(%)
(-)5% 0.2 -1.0
0% 0.2 0.0
5% 0.4 2.0
10% 0.2 2.0
1.0 3.0
RISK
RISK = VOLATILITY
2 Main measures
Describe
- Standard Deviation (MPT) Probability of outcome
- Beta (CAPM)
-Standard Deviation measures how widely the actual return on an investment varies around the mean.
- If returns stay close to the mean, it will have a low SD and be regarded as low risk
- Returns fluctuating widely around the mean would have a high SD and be regraded as high risk
Calculated by taking square root of variance
Ie variance of 30.60 = -/30.60 = 5.53 SD
Standard and mean average returns are 15% Deviation (SD)
Expected returns : Assume that portfolio has SD of 7% and mean returns are 15%
3 percentages?
There will be :
- a 68% chance that the actual return will lie somewhere between 8% and 22% (15%+- 7)
- Around a 95% chance that the actual return will lie somewhere between 1% and 29%
(15% +- 2 x 7)
- a 99% chance that actual return will lie somewhere between -6% and 36% (15% +-3x7)
1 SD - 68%
2 SD- 95%
3 SD- 98%
Standard Deviation is saying given the returns in the past, statistically, it should do x in future
Correlation
What is range
What is
- Most effective diversification come from combining negatively correlated investments
Drawbacks
- Correlation is number between +1 and -1
+ 1 positively correlated (Lloyds & Barclays)
-1 negatively correlated (ice cream umbrellas)
Whilst reduce risk by having negatively correlated , reduce/cancel out performance. So ideally need an element of negative correlation, but not exactly.
0 = Uncorrelated
Drawbacks - simplistic, rely upon historic data - in major financial crisis, all assets may fall to zero as correlations move to + 1
Need element of negative correlation, -1 would cancel each other out
Standard Deviation Calculation
4 Steps
How do you work out variance from SD
- Work out mean eg 5+10+15+20+25 /5 = 15
Step 1: Deduct Mean from each return 5-15 = -10 10-15 = - 5 15-15 = 0 20-15 = 5 25-15 = 10 Step 2: Square the answers Step 3: Add up answers to Step 2 100+25+0+25+100 = 250 Step 4: Divide answer of step 3 by n (no of figs) 250/5 = 50 Variance = 50 Standard Deviation is square root of variance. (SD2 is variance) ~/50 = 7.07 68% returns 15 +- 7.07 (SD from MEAN)
Summary:
1. Calculate difference between actual and expected (mean)return
2. Square difference to eliminate minuses
3. Sum the result and divide by n
4 Sum result = variance
Variance - SD2 (squared)
What is standard Deviation
Covariance
Calculation using the mean as expected return then risk measured by level of dispersion from the expected/average value. SD is measure of total risk of an individual security
Low risk = returns do not fluctuate significantly around mean = small SD
High risk= returns fluctuate significantly around mean = large SD
- Measures how much actual return on an investment varies around mean
- Calculated by difference between mean and actual
- SD calculates volatility
- if SD =3 & mean 10 : 68% of results would be between 7% & 13%
Covariance : SDa x SDb x correlation coefficient
Three main methods to determine risk adjusted return:
A) Information ratio
B) Sharpe Measure
C) Alpha (Jensens Alpha)
Information Ratio
Formula
Purpose
Rp - Rb ————- Reaching error Or... Average annual portfolio return (Rp)- average annual benchmark return(Rb) —————————————————————————————— Tracking error
Information ratio: Compares the excess return achieved by the fund over a benchmark portfolio to the fund’s tracking error ( calculated as SD of excess return over benchmark).
It is a risk adjusted return measured to evaluate the fund manager’s relative experience
Fred’s OEIC return 10%, compared to 9.5% from benchmark. Tracking error 0.9
10% - 9.5% = 0.56
—————-
0.9
OEIC beat its benchmark and active management has in effect been justified.
Return
Purpose:
- Compare against sector/benchmark
- assess risk adjusted returns
- Out performance /added alpha
- Consistency of fund manager
Sharpe Ratio
Formula
What is it
Sharp ratio:
Return on investment- risk free return
——————————————————-
Standard deviation of return on return of investment
HIGHER SHARP IS MORE ATTRACTIVE
Return for each unit of risk
Adjusts rates of return to take account of riskiness of investment or fund. Ratio measures excess returns for every unit of risk, measured by SD (total risk) which is taken to achieve the return.
Sharp ratio calculates the excess return achieved by a fund (ie return over and above risk free return) for each unit of total risk (SD)
Example: 2 funds, both average return 12% - Fund A has SD 6, Fund B has SD of 8. RFR is 6%
Fund A Sharpe = (12% - 6%) / 6 = 1
Fund B Sharp = (12% - 6%) / 8 = 0.75
Fund A better value than Fund B (higher ratio is better)
GH:
Fred’s OEIC returned 10% annualised. Compared to 4% risk free. SD 8%
10% - 4% = 0.75
————-
8%
Meaning OEIC returned just 0.75% return above risk free rate - hardly worth it
Limitations of Sharpe Ratio (5)
- SD assumes that’s equity/investment returns are normally distributed- they aren’t
- Sharpe can be manipulated by changing measurement interval
- simplistic single figure
- Ignore investment charges and costs
- historic
Alpha
Formula
Definition
Alpha = Rportolio/Equity return - Rcapm
CANT DO ALPHA WITHOUT DOING CAPM
- Measure of fund managers stock picking skills
- Return not explained by CAPM
- Higher the alpha the better
- Alpha indicates hoe much return manager has made independent of the market
Example fund average annual return 6%, risk free rate 1%, expected market return is 5%. beta is 0.9%
Alpha = 6 (Rportfolio) - {1 +0.9(5-1) = 1.4%
Efficient Frontier
Limitations (6)
3 inputs required
Optimum level of return for given level of risk
- Theoretical line
- Historic data
- can you predict accurately
- Reliant on risk questionnaire
- Assumes Standard Deviation is measure of risk
- Excludes cost and charges
- Assumes portfolio uses passives
3 inputs required - Expected return - Correlation - Standard deviation /level of risk -
Performance Attribution (5 steps)
- Select appropriate benchmark
- Establish asset allocation for benchmark fund
- Calculate return for each asset class in benchmark fund
- Compare benchmark to actual portfolio performance in terms of asset allocation
- Calculate the effect of stock selection or sector choice
Selecting Benchmark :
- criteria / considerations (5)
What do benchmarked provide (3)
`limitations (5)
- Specified and agreed in advance with client
- Priced at suitable periods - How often calculated
- How has benchmark performed in past - availability of historic data
- How is benchmark calculated - should be transparent
- Benchmark should be relevant to investment fund/portfolio
Benchmarks provide:
- Measure to compare performance of different types of fund
- basis for reviewing asset allocation and structure of portfolio with fund manager or stockholder
- benchmark for assessing and comparing the performance of DFMs
Limitations:
- No two portfolios same
- Portfolios may differ in terms of asset classes
- SOme PFS closely reflect benchmark, others not so
- MAnagers have wide discretion over benchmark used
- Benchmarks don’t allow for dividend payments
- Benchmarks do not allow for costs
- PFS may differ in terms of risk applied (as measured by Beta)
- set asset allocation
- independent /neutral agreed basis
- manage risk expectation
- measure relative performance
- added performance by fund manager
