Quant - Rates & Returns

Question 1

What are three interpretations of an interest rate?

Answer 1

An interest rate, r, can have three interpretations:
(1) a required rate of return,
(2) a discount rate,
(3) an opportunity cost.
An interest rate reflects the relationship between differently dated cash flows.

Question 2

How does an interest rate relate to the risk-free rate and other premiums?

Answer 2

An interest rate can be viewed as the sum of the real risk-free interest rate and a set of premiums that compensate lenders for bearing distinct types of risk.

Question 3

What are the four types of premiums that usually make up an interest rates premium?

Answer 3

Remember “MILD”:
Maturity premium
Inflation premium
Liquidity premium
Default risk premium

Question 4

How do you calculate the nominal risk-free interest rate?

Answer 4

The nominal risk-free interest rate is approximated as the sum of the real risk-free interest rate and the inflation premium.

Question 5

What are the two components of an asset’s return?

Answer 5

(1) In income yield consisting of cash dividends or interest payments
(2) a return reflecting the capital gain or loss resulting from changes in the price of the financial asset

Question 6

What is the “holding period return”?

How do you calculate it?

Answer 6

A holding period return, R, is the return that an investor earns for a single, specified period of time (e.g., one day, one month, five years).

Question 7

Consider the following means for a dataset:

Arithmetic mean
Geometric mean
Harmonic mean
Trimmed mean
Winsorized mean

What drives the choice of which of the various alternative measurements of mean to use?

Answer 7

The choice of which of the various alternative measurements of mean to use for a given dataset depends on considerations such as:

(1) Presence of extreme outliers;
(2) Outliers that we want to include;
(3) Whether there is a symmetric distribution;
(4) Whether we want to capture the impact of compounding.

Question 8

What is the purpose of the money-weighted return?

How do you calculate it?

Answer 8

Purpose:
The actual return earned on an investment after accounting for the value and timing of cash flows.

Calculation:
Use IRR on the calculator.

Question 9

What does a time-weighted return measure?

How do you calculate it?

Whats the formula for N items in a dataset?

Answer 9

Purpose:
A time-weighted return measures the compound rate of growth of one unit of currency invested in a portfolio during a stated measurement period.

Calculated By:
Geometric Mean

Formula:

Question 10

What is the benefit of Time-Weighted returns to Money-Weighted Returns?

Answer 10

Unlike a money-weighted return, a time-weighted return is not sensitive to the timing and amount of cashflows

Question 11

Would a portfolio manager prefer a time-weighted return or money-weighted return?

Answer 11

Answer:
A time-weighted return.

Why?
Cash withdrawals or additions to the portfolio are generally outside of the control of the portfolio manager.

Question 12

What is the benefit or purpose of annualizing periodic returns?

Answer 12

Annualizing periodic returns allows investors to compare different investments across different holding periods to better evaluate and compare their relative performance.

Question 13

What equation is used to calculate the annualized periodic return?

Answer 13

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Question 14

If given two returns with two different time horizons, how would you compare them.

Ex:
Option 1: 1% return / month for 8 months
Option 2: 0.50% return / week for 32 weeks (i.e., 8 months)

?

Answer 14

Calculate the annualized period return and compare results.

Question 15

How do you calculate a manager’s “NET RETURN”?

Answer 15

The gross return less managerial and administrative expenses

Question 16

Would a portfolio prefer to be measured by their “GROSS RETURN” or “NET RETURN”?

Answer 16

Gross return, as it is taken before managerial and admin expenses and thus makes comparing returns to other shops more comparable.

Question 17

Which return is more important to the investor’s bottom line “GROSS RETURN” or “NET RETURN”?

Answer 17

Net return as it is a better return measure of what an investor actually earned.

Question 18

How do you calculate a firm’s “GROSS RETURN”

Answer 18

Gross Return = [ Final - Initial ] / Initial

Question 19

How do you calculate an investors “AFTER TAX NET RETURN”?

Answer 19

The after-tax nominal return is computed as the total return minus any allowance for taxes on dividends, interest, and realized gains.

Question 20

What is the purpose of “REAL RETURN”?

How do you calculate it?

Answer 20

Purpose:
The Real Rate of Return (%) measures the percentage return earned on an investment after adjusting for the inflation rate and taxation, unlike the nominal rate.

Calculation:
Real Rate of Return = (1 + Nominal Rate) ÷ (1 + Inflation Rate) – 1

Question 21

Why are “REAL RETURNS” useful?

Answer 21

Real returns are particularly useful in comparing returns across time periods because inflation rates may vary over time and are particularly useful for comparing investments across time periods and performance between different asset classes with different taxation.

Question 22

How do you calculate the “ARITHMETIC RETURN”?

When is it useful?

Answer 22

Calculation:
see image

When Useful:
Short-Term Investments: When analyzing investments held for a short duration, such as a few days or months, the arithmetic return is a straightforward and effective measure. It simply reflects the gain or loss over the period without the need to account for compounding effects.

Question 23

How do you calculate the “GEOMETRIC MEAN RETURN”?

Answer 23

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Question 24

What is the purpose of the “HARMONIC MEAN”?

How do you calculate it?

Answer 24

Purpose:
The harmonic mean is ideally suited for scenarios where average rates or ratios need to be calculated accurately without being disproportionately affected by outliers or extreme values. It’s a powerful tool in the portfolio analyst’s toolkit, particularly useful for financial ratios and rates that need to be averaged in an equitable manner.

Calculation:
It is the reciprocal of the arithmetic mean of the reciprocals

Question 25

Create the flow chart for deciding which type of return to use

Answer 25

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Question 26

If given weekly returns, how do you convert to annual returns?

Answer 26

R_ANNUAL = (1+R_WEEKLY)^52 - 1

Question 27

If given daily returns, how do you convert to weekly returns?

Answer 27

R_WEEKLY = (1+R_DAILY)^5 -1

Question 28

What is the general equation for computing an annualized return from a general period return?

Answer 28

R_ANNUAL =(1+R_PERIOD)^(PERIODS_PER_YEAR) - 1

Question 29

How do you calculate the continuously-compounding return from the holding period return?

Answer 29

An important concept is the continuously compounded return associated with a holding period return, such as R1. The continuously compounded return associated with a holding period return is the natural logarithm of one plus that holding period return, or equivalently, the natural logarithm of the ending price over the beginning price (the price relative).

Question 30

What type of expenses are included in the portfolio manager’s gross return?

Answer 30

Trading expenses, however, such as commissions, are accounted for in (i.e., deducted from) the computation of gross return because trading expenses contribute directly to the return earned by the manager. Thus

Question 31

How do you calculate the “nominal rate” given:
1. risk-free rate
2. inflation

Answer 31

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Question 32

How do you calculate the “real return” given:
1. risk-free rate
2. inflation
3. risk premium

Answer 32

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Question 33

How do you calculate an investors leveraged return?

Answer 33

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Question 34

What is the physical interpretation of “leveraged return”?

Answer 34

The return on an investor’s equity, considering the overall return of the portfolio, including the affects of leverage.