Portfolio Performance and DFM Flashcards
What is standard deviation? What is the formula for the SD of a sample
How widely dispersed the possible outcomes are around the mean expected outcome.
Risk is measured as the variability of returns around the mean. If the expected level of return is calculated as the average return (the mean), then the risk is measured as the SD of returns over time.
SD = sqrt(x-mean(x))^2 / n
SD of a sample = sqrt(x-mean(x))^2 / (n-1)
steps for calculating SD where the probability of a return is involved?
1.Establish the average or mean return but weighted for the frequency of
occurrence – we do this by multiplying the total return by the probability to produce a
weighted average - sum weighted averages to find mean.
2.Find the difference of the return in each year from the arithmetic mean and then square it.
- Factor back in the probability of occurrence to produce the probability weighted dispersion of returns – that is the difference squared multiplied by the probability.
- The sum of the squares of the probability-weighted dispersions and the square root
of this represents the standard deviation
What is the three sigma rule?
For normally distributed data, almost all the data points will fall within three standard deviations on either side of the mean.
More specifically, you’ll find:
68% of data within 1 standard deviation;
95% of data within 2 standard deviations ; and
99.7% of data within 3 standard deviations.
What are the characteristics of a normal distribution?
The mean and median are equal.
The mean and variance completely describe the distribution.
68.3% of observations lie between (mean ± 1 standard deviation).
95.5% of observations lie between (mean ± 2 standard deviations).
99.75% of observations lie between (mean ± 3 standard deviations).
Formula for Covariance and correlation?
Covariance = measures direct of relationship between two variables
covariance = sum(x-mean(x)) x sum(y-mean(y)) / (n-1)
Correlation = strength of direction
r = Cov(x,y) / (Sdx x sdy)
What is the information ratio and how is it calculated?
Compares the excess return achieved by the fund over a benchmark portfolio to the fund’s tracking error. Risk-adjusted measure to evaluate the fund manager’s relative experience.
IR = Rp - Rb / tracking error
Rp = portfolio return
Rb = benchmark return
The higher the positive IR the better the risk-adjusted return based on performance relative to the benchmark. Thus, the higher the value added by the manager through active management, based on the amount of risk taken relative to the benchmark.
What is the Sharpe Ratio and how is it calculated?
Measures the excess return for every unit of risk that is taken in order to achieve the return.
return on investment - risk-free return / SD of return on investment
The higher the Sharpe ratio, the better the return on an investment compensates an investor for
the risk taken. A negative Sharpe ratio indicates that a risk-free asset would have performed
better than the investment being analysed.
If manager A generates a return of 14%, while manager B generates a return of 11%, it would appear that manager A has a better performance. However, if manager A, who produced the 14% return, took greater risk than manager B, it may not actually be the case that manager A has a better risk-adjusted return.
The Sharpe ratio for manager A = 1.25
The Sharpe ratio for manager B = 1.40
Manager B was able to generate a higher return on a risk adjusted basis.
What is alpha and how is it calculated?
The difference between the return that would be expected from a security, given its beta, and the return that it has actually produced. It is the part of the return that cannot be explained by movements in the overall market. This is sometimes referred to as the ‘value added’ of the fund manager.
It is the return not measured by the CAPM.
a = actual portfolio return - (Rf + B x (Rm -Rf)
Rf = risk free rate of return
B = beta
Rm = market return
A positive alpha indicates that the security has performed better than would have been predicted given its beta.
A negative alpha indicates that it has performed worse than would have been predicted by its beta.
If you are asked to calculate the annual volatility of a client portfolio, what is being asked of you?
Likely to be given the variance figure.
Volatility is the square root of the variance = SD
Calculating benchmark and portfolio performance.
How would the performance of a portfolio fund manager (FM) be compared to a benchmark in terms of:
Asset allocation
Stock selection / sector choice
Asset allocation:
FM asset allocation x index performance for asset = contribution of manager’s asset class
This can be compared to the index asset allocation x index performance, to see if it over or under achieved.
Stock Selection/sector choice:
index asset allocation x index performance = potential return
index asset allocation x FM performance = FM selection return
What is holding period return?
The holding period return is the return earned over the time an investment is held, expressed as a percentage of the original cost. The holding period return equals the total of all income received during the period plus capital gain or profit, as a percentage of the original investment.
It doesn’t allow for tax or timing of receipts
What is the money weighted return and what are the drawbacks?
The MWR is a modified form of the holding period return formula and is used to calculate the return over the year, adjusting for cash flows.
The MWR method of measuring returns is not considered appropriate when trying to evaluate and compare different portfolios.
This is because it is strongly influenced by the timing of cash flows − this timing could be outside of the fund manager’s control and is often decided by the client.
It does not identify whether the overall return for the investor is due to the ability of the fund manager or as a result of when additional funds were invested.
What is time weighted return?
TWR can compare the performance of one fund manager to that of another by eliminating the distortions caused by the timing of new money. It does this by breaking down the return for a particular period into sub-periods between each addition or withdrawal of capital.
What are indexes used for?
- monitoring market performance;
- comparing the performance of a particular share with its sector or with the market as a whole;
- comparing the performance of a fund manager with the performance of the market as a whole;
- constructing index funds; and
- measuring systematic risk (beta).
How are marked weighted indexes calculated and what is their disadvantage?
summation of the market values or capitalisations (calculated by multiplying the share price by the number of shares outstanding for each company).
A disadvantage of market-value-weighted indices is that companies whose share prices have risen will, all other things being equal, be a larger part of the index than ones whose share prices have fallen. Therefore, index funds or active funds benchmarked against an index tend to ‘overweight’ companies that have already been successful investments and ‘underweight’ companies that have been neglected by investors.
