LM1 Time value of money

Question 1

What are the 3 ways that interest rates (r) can be thought of?

Answer 1

1. Required rate of return
2. Discount rate
3. Opportunity cost

Question 2

What are the 5 continuously changing determinants of interest rates?

Answer 2

1. Real default risk-free rate (over a single period)
2. Inflation premium
3. Default risk premium
4. Liquidity premium
5. Maturity premium

Question 3

What is the maturity premium?

Answer 3

Compensation for greater price sensitivity from changes in rates

Question 4

What is pi^e?

Answer 4

The default risk-free rate plus the inflation premium

Question 5

Over what time period are interest rates quoted?

Answer 5

Always annual

Question 6

How do you calculate holding period return?

Answer 6

R = [(ending price - beginning price) + all income] / beginning price

Question 7

How do you calculate multi-period holding period of return?

Answer 7

• Find the return for each holding period
• add 1 to each
• multiply them together
• subtract 1 at the end

Question 8

How do you calculcate arithmetic return?

Answer 8

Add up all your returns and divide by T

Question 9

How do you calculate geometric mean return?

Answer 9

• Take return from each period and add 1
• Multiply them together
• Put the number to the power of 1/T
• Subtract 1

Question 10

When is the geometric mean equal to the arithmetic mean?

Answer 10

When all observations are equal. When there is variability, GM < AM

Question 11

When would you use a geometric mean return?

Answer 11

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

Question 12

How do you get from the formula for arithmetic mean to the one for harmonic mean?

Answer 12

AM = sum(x) / n

1. Invert the x:

sum(1/x) / n

2. Invert the whole fraction:

n / sum(1/x)

Question 13

Why is harmonic mean useful for reducing the effect of outliers?

Answer 13

• Observation weight is inversely proportional to its magnitude for HM.
• Therefore it reduces the effect of outliers

Question 14

How can harmonic mean be used to deal with dollar cost averaging?

Answer 14

• 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

Question 15

If I have a 6% trimmed mean and an untrimmed set of 200 observations, how many would I have in my yrimemd set?

Answer 15

176
200 - (6% x 2 x 200)

Question 16

Why is trimmed mean used commonly in economic data like CPI?

Answer 16

• Gets at the stable core of prices
• Removes a % from both the largest and smallest

Question 17

What is a winsorized mean?

Answer 17

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

Question 18

What is the money-weighted return?

Answer 18

• 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

Question 19

What is time-weighted return?

Answer 19

• 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

Question 20

How do you determine continuously compounded rate of return?

Answer 20

ln (100 + return% / 100) = continuously compounded rate of return

Question 20

What is the difference between gross and net return?

Answer 20

• 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

Question 20

What is the formula to calculate real return?

Answer 20

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)

Question 21

What is the formula for calculating the risk premium?

Answer 21

1 + nominal return / 1 + risk free rate = 1 + risk premium

Question 22

What is the after-tax real return?

Answer 22

• Investor measure of growth in purchasing power of portfolio
• After tax return less inflation
• Important metric for large investors like endowments

Question 23

How can portfolio leverage be obtained?

Answer 23

• Margin loans
• Derivatives (can contain built-in leverage)
• Collateralised loans (repos)

Question 24

Under what conditions does leverage enhance return?

Answer 24

If RsubP > RsubD
I.e., if the portfolio return is greater than the cost of debt.

Question 25

What is a carry trade?

Answer 25

• 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

Question 26

How do you calculate return on a leveraged portfolio?
- 50m stock portfolio
- 9% return
- 5% borrowing cost
- 40% debt

Answer 26

Leveraged return = portfolio return + (spread x debt/equity)

RsubL = 9% + (9%-5%)*(30m/20m)
RsubL = 15%