Module 1 Rates & Returns

Question 1

What are three ways to think of interest rates?

Answer 1

Required rate of return
Discount rate
Opportunity cost

Question 2

What is an interest rate?

Answer 2

A rate of return that reflects the relationship between differently dated cash flows.

Question 3

What is the required rate of return?

Answer 3

The minimum rate of return an investor must receive to accept an investment.

Question 4

What are discount rates?

Answer 4

A rate of return that reflects the relationship between differently dated cash flows.

Question 5

What are opportunity costs?

Answer 5

The value that investors forgo by choosing a course of action. If a party decide to spend money today, he forfeits potential interest he could have received on that money.

Question 6

What are the components of an interest rate?

Answer 6

Real Risk-Free Interest Rate + Inflation Premium + Default Risk Premium + Liquidity Premium + Maturity Premium

Question 7

What is the real risk-free interest rate?

Answer 7

The single-period interest rate for a completely risk-free security if no inflation were expected.

Question 8

What is the inflation premium?

Answer 8

A premium that compensates investors for the expected inflation and reflects the average inflation rate expected over the maturity of the debt.

Question 9

What is the default risk premium?

Answer 9

A premium that compensates investors for the possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount.

Question 10

What is the liquidity premium?

Answer 10

A premium that compensates investors for the risk of loss relative to an investment’s fair value if the investment needs to be converted to cash quickly. Illiquid assets often contain a liquidity premium.

Question 11

What is the maturity premium?

Answer 11

A premium that compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended. Often a positive maturity premium on longer-term debt.

Question 12

What is the nominal risk-free interest rate?

Answer 12

Real risk-free rate + inflation premium

Question 13

How is the nominal risk-free rate represented in real life?

Answer 13

By short-term government debt

Question 14

How are interest rates typically quoted?

Answer 14

Annually, that means that a 3% T-Bill over 90 days means an annual 3% interest.

Question 15

What are the two components of a financial asset’s total return?

Answer 15

Income yield such as dividend or interest + Capital gain or loss reflecting the underlying price of the asset.

Question 16

What is a Holding Period Return?

Answer 16

The return earned from holding an asset for a single specified period of time.

Question 17

How to calculate a Holding Period Return?

Answer 17

( (Price at T1 - Price at T0) + Income Yield ) / Price at T0

Question 18

How to compound Holding Period Returns?

Answer 18

Multiplying

Question 19

What is Arithmetic Return or Mean Return?

Answer 19

Normal average return, denoted by R with a bar above.

Question 20

What is Geometric Mean Return?

Answer 20

The compound rate of return. An average return that includes the previous year’s earnings into the base amount. A way to calculate compound returns.

Question 21

What is an advantage of Geometric Mean over Arithmetic Mean?

Answer 21

Geometric mean includes gains or losses from the previous period into the calculation which makes it more appropriate for portfolio performance measurement.

Question 22

What is a disadvantage of the Arithmetic Mean?

Answer 22

It is biased upwards unless each of the underlying holding period returns is equal. The bias is particularly severe if the returns are both positive and negative.

Question 23

What is the Harmonic Mean?

Answer 23

The Harmonic Mean is appropriate in cases in which the variable is a rate or a ratio. Think of Cost Averaging Example.

Question 24

What is an advantage of Harmonic Mean?

Answer 24

It is not influenced much by outliers.

Question 25

How are Arithmetic, Harmonic and Geometric Mean mathematically related to each other?

Answer 25

Arithmetic Mean * Harmonic Mean = Geometric Mean Squared

Question 26

How to calculate the Geometric Mean?

Answer 26

Multiply all numbers between brackets and square it with 1/n

Question 27

How to calculate Harmonic Mean?

Answer 27

Divide n by the sum of 1/X between brackets.

Question 28

What is Trimmed Mean?

Answer 28

The trimmed mean removes a small defined percentage of the largest and smallest values from a dataset before calculating the normal mean.

Question 29

What is Winsorized Mean?

Answer 29

Calculate normal mean after replacing extreme values at both ends with the values of their nearest observations.

Question 30

When to use Arithmetic Mean, Geometric Mean, or Harmonic / Trimmed / Winsorized Mean?

Answer 30

When you want to include all values = Arithmetic Mean
When there is compounding = Geometric Mean
When there are extreme outliers = Harmonic / Trimmed / Winsorized

Question 31

What is the money-weighted return?

Answer 31

A return that accounts for the money invested and places more emphasis on periods with more money invested. Gives investors more information on the actual return on her investment.

Question 32

How to calculate the money-weighted return?

Answer 32

Discount all cash flows back to the present value and set present value equal to zero.

Question 33

What is the internal rate of return?

Answer 33

Equal to money-weighted rate of return. The discount rate at which the sum of present values is equal to zero.

Question 34

What is the time-weighted rate of return?

Answer 34

The return that compounds returns over sub-periods together, with each period weighted according to its duration.

Question 35

How to calculate the time-weighted rate of return?

Answer 35

Multiply the returns of each period + 1 and finally subtract one again.

Question 36

What is the continuously compounded return?

Answer 36

The natural logarithm of one plus the ending price over the beginning price (actual return).

Question 37

What is the gross return of asset managers?

Answer 37

The return earned by the asset manager before any deductions like fees or taxes. However, trading commissions are deducted.

Question 38

What is the net return of an asset manager?

Answer 38

The return after all deductions, net return for investors.

Question 39

How to calculate the Leveraged Return?

Answer 39

Leveraged Return = Portfolio Return + ( Borrowed Value / Equity Value ) * (Portfolio Return - Interest)