Quant - Rates & Returns Flashcards
What are three interpretations of an interest rate?
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.
How does an interest rate relate to the risk-free rate and other premiums?
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.
What are the four types of premiums that usually make up an interest rates premium?
Remember “MILD”:
Maturity premium
Inflation premium
Liquidity premium
Default risk premium
How do you calculate the nominal risk-free interest rate?
The nominal risk-free interest rate is approximated as the sum of the real risk-free interest rate and the inflation premium.
What are the two components of an asset’s return?
(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
What is the “holding period return”?
How do you calculate it?
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).
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?
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.
What is the purpose of the money-weighted return?
How do you calculate it?
Purpose:
The actual return earned on an investment after accounting for the value and timing of cash flows.
Calculation:
Use IRR on the calculator.
What does a time-weighted return measure?
How do you calculate it?
Whats the formula for N items in a dataset?
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:
What is the benefit of Time-Weighted returns to Money-Weighted Returns?
Unlike a money-weighted return, a time-weighted return is not sensitive to the timing and amount of cashflows
Would a portfolio manager prefer a time-weighted return or money-weighted return?
Answer:
A time-weighted return.
Why?
Cash withdrawals or additions to the portfolio are generally outside of the control of the portfolio manager.
What is the benefit or purpose of annualizing periodic returns?
Annualizing periodic returns allows investors to compare different investments across different holding periods to better evaluate and compare their relative performance.
What equation is used to calculate the annualized periodic return?
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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)
?
Calculate the annualized period return and compare results.
How do you calculate a manager’s “NET RETURN”?
The gross return less managerial and administrative expenses
Would a portfolio prefer to be measured by their “GROSS RETURN” or “NET RETURN”?
Gross return, as it is taken before managerial and admin expenses and thus makes comparing returns to other shops more comparable.
Which return is more important to the investor’s bottom line “GROSS RETURN” or “NET RETURN”?
Net return as it is a better return measure of what an investor actually earned.
How do you calculate a firm’s “GROSS RETURN”
Gross Return = [ Final - Initial ] / Initial
How do you calculate an investors “AFTER TAX NET RETURN”?
The after-tax nominal return is computed as the total return minus any allowance for taxes on dividends, interest, and realized gains.
What is the purpose of “REAL RETURN”?
How do you calculate it?
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
Why are “REAL RETURNS” useful?
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.
How do you calculate the “ARITHMETIC RETURN”?
When is it useful?
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.
How do you calculate the “GEOMETRIC MEAN RETURN”?
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What is the purpose of the “HARMONIC MEAN”?
How do you calculate it?
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
Create the flow chart for deciding which type of return to use
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If given weekly returns, how do you convert to annual returns?
R_ANNUAL = (1+R_WEEKLY)^52 - 1
If given daily returns, how do you convert to weekly returns?
R_WEEKLY = (1+R_DAILY)^5 -1
What is the general equation for computing an annualized return from a general period return?
R_ANNUAL =(1+R_PERIOD)^(PERIODS_PER_YEAR) - 1
How do you calculate the continuously-compounding return from the holding period return?
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).
What type of expenses are included in the portfolio manager’s gross return?
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
How do you calculate the “nominal rate” given:
1. risk-free rate
2. inflation
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How do you calculate the “real return” given:
1. risk-free rate
2. inflation
3. risk premium
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How do you calculate an investors leveraged return?
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What is the physical interpretation of “leveraged return”?
The return on an investor’s equity, considering the overall return of the portfolio, including the affects of leverage.
