LM1 Time value of money Flashcards
What are the 3 ways that interest rates (r) can be thought of?
- Required rate of return
- Discount rate
- Opportunity cost
What are the 5 continuously changing determinants of interest rates?
- Real default risk-free rate (over a single period)
- Inflation premium
- Default risk premium
- Liquidity premium
- Maturity premium
What is the maturity premium?
Compensation for greater price sensitivity from changes in rates
What is pi^e?
The default risk-free rate plus the inflation premium
Over what time period are interest rates quoted?
Always annual
How do you calculate holding period return?
R = [(ending price - beginning price) + all income] / beginning price
How do you calculate multi-period holding period of return?
- Find the return for each holding period
- add 1 to each
- multiply them together
- subtract 1 at the end
How do you calculcate arithmetic return?
Add up all your returns and divide by T
How do you calculate geometric mean return?
- Take return from each period and add 1
- Multiply them together
- Put the number to the power of 1/T
- Subtract 1
When is the geometric mean equal to the arithmetic mean?
When all observations are equal. When there is variability, GM < AM
When would you use a geometric mean return?
When looking at a return over a number of periods.
This is because if you compound the arithmetic mean it does NOT equal the return over multiple periods
How do you get from the formula for arithmetic mean to the one for harmonic mean?
AM = sum(x) / n
- Invert the x:
sum(1/x) / n
- Invert the whole fraction:
n / sum(1/x)
Why is harmonic mean useful for reducing the effect of outliers?
- Observation weight is inversely proportional to its magnitude for HM.
- Therefore it reduces the effect of outliers
How can harmonic mean be used to deal with dollar cost averaging?
- Helps calculate average cost per share
- if you average the prices paid per share using AM you don’t get to the true average price
If I have a 6% trimmed mean and an untrimmed set of 200 observations, how many would I have in my yrimemd set?
176
200 - (6% x 2 x 200)
Why is trimmed mean used commonly in economic data like CPI?
- Gets at the stable core of prices
- Removes a % from both the largest and smallest
What is a winsorized mean?
Replaces extreme values at both ends with cutoff values
E.g. if I have 100 observations and an 8% winsorized mean, I replace obs 1-8 with value of obs 9, and replace obs 93-100 with value of obs 92
What is the money-weighted return?
- AKA yield to maturity
- Accounts for magnitude and timing of investment (weighting return based on size of each investment along the holding period)
- Can use Excel’s IRR formula to calculate
What is time-weighted return?
- A comparable and standardised measure of return: the growth of $1 over a given time period
- Comparable across investments
- Calculated by breaking investment period into holding periods, broken by any significant cash inflows or outflows
Compound the holding period returns (HPS) and express return annually
How do you determine continuously compounded rate of return?
ln (100 + return% / 100) = continuously compounded rate of return
What is the difference between gross and net return?
- Gross return represents particular skill of the manager in earning a return (after trading costs incurred by manager, but before management fees are taken)
- Net return is what investor earns after expenses are paid
- Difference is the cost of choosing that manager
- Returns are quoted pre-tax because of differences in tax rate brackets
What is the formula to calculate real return?
1 + real return = 1 + nominal rate / 1 + inflation rate
Inflation rate is typically period over period CPI (check which price index they’re using for comparability across funds)
What is the formula for calculating the risk premium?
1 + nominal return / 1 + risk free rate = 1 + risk premium
What is the after-tax real return?
- Investor measure of growth in purchasing power of portfolio
- After tax return less inflation
- Important metric for large investors like endowments
How can portfolio leverage be obtained?
- Margin loans
- Derivatives (can contain built-in leverage)
- Collateralised loans (repos)
Under what conditions does leverage enhance return?
If RsubP > RsubD
I.e., if the portfolio return is greater than the cost of debt.
What is a carry trade?
- Borrowing in a currency it is cheap to borrow in, investing in a currency with good returns
- I.e., borrow in yen, invest in dollars
- This ensures that portfolio return is greater than cost of debt
How do you calculate return on a leveraged portfolio?
- 50m stock portfolio
- 9% return
- 5% borrowing cost
- 40% debt
Leveraged return = portfolio return + (spread x debt/equity)
RsubL = 9% + (9%-5%)*(30m/20m)
RsubL = 15%
