Lecture 2 Flashcards
To establish the level of risk we should find in the marketplace
Use historical experience to forecast, there is no theory about the level of risk
Are expected returns/ risk directly observable?
No
Can we observe realised rates of return?
Yes
Total risk-free return formula =
(Par value) / P(T) ) - 1
Investment returns are expressed as
Effective annual rate (EAR)
Effective annual rate (EAR) shows
% increase in funds invested over a 1 year horizon
Gross return =
Terminal value of a $1 investment
EAR formula =
EAR = rf(1)
Gross return formula =
(1 + EAR)
Annual percentage rate (APR) shows
Annual rate charged for borrowing or earned through an investment
As T (years) approaches zero
Effectively approach continuous compounding. The relationship between EAR and APR given by the exponential function.
Holding period =
How long an individual holds an investment for
Realised rate of return depends on (2)
- Price per share at period’s end
- Cash dividends collected over the year
Holding period return assumes
All dividends are received at the end of the period
Holding period return formula =
[ (Ending price of share - starting price) + Cash dividend ] / Starting price
Holding period return ignores
Reinvestment income earned between receipt payment and end holding period if dividends are received during the period
Dividend yield =
% return from dividends
Holding period return simple formula =
Dividend yield + Rate capital gains
Standard deviation of the rate of return is
A measure of risk
Standard deviation =
Square root of variance
Variance =
Expected value of squared deviations from expected returns. Provides measure of uncertainty of outcomes.
Higher the volatility
Higher the variance
Standard variance is a reasonable measure of risk as long as
The probability distribution is symmetric about the mean
Risk premium =
Expected return - risk free rate
Excess return =
Actual rate of return - actual risk free rate
Risk premium is an estimate for
The value of excess return
Risk aversion =
Degree to which investors willing to commit funds to stock
If the risk premium = 0
Investors wouldn’t invest > risk averse
Geometric average return =
Measure of performance (fixed annual HPR) which compounds over a period to a terminal value
Arithmetic average return =
Arithmetic average of a sample of rates of return
Larger the swings in rates of return
Greater the discrepancy between arithmetic and geometric averages
3 types of means
- Expected
- Arithmetic
- Geometric
Sharpe ratio
The importance of the trade off between reward (risk premium) and risk (measured by s.d) suggests that we measure the attraction of a portfolio by a ratio of risk premiums to s.d. of excess returns
Sharpe ratio formula =
Risk premium / SD of excess returns
Sharpe ratio widely used
To evaluate performance of investment managers
When the distribution is positively skewed
Standard deviation overestimates risk due to extreme positive surprises (which don’t concern investors) but increase the estimate of volatility
Kurtosis measures
The degree of fat tails
Any kurtosis above 0 (excess)
Sign of fatter tails
Value at risk (VaR) =
Measure of the risk of loss for investments
Value at risk is (2)
- The most optimistic measure of risk > as it takes the highest return (smallest loss)
- More realistic > expected loss of downside exposure
This is called expected shortfall (ES) or conditional tail expectation (CTE)
