Module 7: Measures of Investment Returns

Question 1

Simple Rate of Return

Answer 1

Divide the total return by the number of years that the investor has held the asset

Question 2

Compound Rate of Return

Answer 2

Assumes that all interim proceeds, such as interest and repayment of principal, are reinvested over the holding period, which can be easily calculated with a financial calculator

Question 3

Arithmetic Mean

Answer 3

The noncompounded return, calculated by dividing the sum of the periodic returns by the total number of periods being evaluated. Does not assume reinvestment of returns. Add returns each year together and divide by n periods.

Question 4

Geometric Mean

Answer 4

Assumes compounding returns. Use calculator:
PV: -1
FV: (1+return year 1)*(1+return year 2)…
N: number of periods
Solve for I/YR

Question 5

Geometric vs. Arithmetic Mean

Answer 5

Note that the geometric mean will always be lower than the arithmetic mean, except when the returns for all periods are equal - in which case the geometric mean and arithmetic means will be equal. When analyzing the security’s returns, the geometric mean would be the preferred measurement over the arithmetic mean

Question 6

Time-Weighted Return

Answer 6

Determined without regard to any subsequent cash flos of the investor, it measures the performance of the investment over a time period (and not of the investor, as in a dollar-weighted approach)

Question 7

Dollar-Weighted Approach

Answer 7

considers the subsequent contributions to and withdrawals from an investment - including the sale of, for example, stock. Focuses more on the return of the investor (not the investment) over a time period and usually results in a rate of return different than the time-weighted method.

Question 8

Nominal Rate of Return

Answer 8

It’s stated rate of return for a given period without accounting for invlation.

Question 9

Real Rate of Return

Answer 9

Takes into account inlation:
((1+Rn)/(1+inflation)-1) * 100
Rn = Absolute Return

Question 10

After-Tax Inflation-Adjusted Rate of Return

Answer 10

Step 1: Compute the after-tax rate of return by using this formula: return after-tax = nominal return * (1-investor’s marginal tax rate (which could include state tax rate))
Step 2: Multiply the Nominal Rate by (1- investor’s marginal tax rate) and use this product as the numerator in the inflation-adjusted rate of return formula and derive the after-tax, inflation adjusted amount.

Question 11

Annual Percentage Rate

Answer 11

The yearly cost of funds expressed as a percentage. However, the nominal APR does not take compounding into consideration.

Question 12

Effective Annual Rate

Answer 12

The annual precentage rate taking into consideration the impact of compounding.

(1+(i/n))^n -1

i = annual interest rate 
n = number of peiods

Question 13

Total Return

Answer 13

Includes the income from dividends or interest plus any capital appreciation over a given time period.

Question 14

SEC Yield

Answer 14

The standardized calculation that the SEC required mutual funds to report and allows investors to compare yields among various investments. It’s yield is based on the most recent 30-day period covered by the fund’s SEC filings, and it represents the interest and dividends earned during that particular period after expenses are been deducted.

Question 15

Holding Period Return

Answer 15

“Single Period Return” is simply the total return of an investment for the given period over which the investment is owned. Major weakness because it fails to consider the timing of when the cash flows actually occured. Holding period of over 1 year: overestimates actual return, holding period under 1 year: underestimates actual return

HPR = (ending value - beginning value + cash flows) / beginning value

Question 16

Risk-Adjusted Return

Answer 16

A simple-risk adjusted return calculation for a stock or mutual fund using beta is to divide the stock or mutual fund’s nominal rate of return by it’s beta coefficient.

Total Return / Beta

Question 17

Jensen’s Alpha

Answer 17

Sometimes simply called Alpha, is a measure of the risk-adjusted value added by a portfolio manager. Measures the portfolio’s actual or realized return in excess of the expected return calculated by the capital asset pricing model (CAPM). Because Beta is used in calculating Jensen’s alpha, it is only appropriate for evaluating diversified portfolios and stocks that constitute diversified portfolio’s.

Question 18

Jensen’s Alpha Calculation

Answer 18

Average rate of return for portfolio P - (risk free ROR + (market’s ROR - RFROR)*Beta for Portfolio P)

Question 19

Treynor Ratio

Answer 19

Uses beta in its denominator and, therefore, may be used only to compare the performance of diversified portfolios or stocks that constitute diversified portfolios. Relative performance measure. Only when it is used to evaluate an asset’s performance relative to another potential investment or a benchmark does it convey useful information. The higher the better

Question 20

Treynor Ratio Calcuation

Answer 20

(average ROR-RFROR)/ Beta for portfolio P

Question 21

Sharpe Ratio

Answer 21

Uses standard deviation in its denominator and, therefore, is a catchall formula that may be used to compare the performance of all portfolio’s. Relative performance measure, the higher the ratio, the better risk-adjusted rate of return. High Sharpe ratios will appear in asset classes that have performed well in the past. Stay within the same asset class when comparing the Sharpe Ratio

Question 22

Sharpe Ratio Calculation

Answer 22

(average ROR - RFROR) / St. Dev

Question 23

Information Ratio

Answer 23

Measure the portfolio’s average rate of return in excess of a comparison portfolio (benchmakr) divided by the standard deciation of the excess return. It measures the active return over active risk. Should only be used when alpha is positive

Question 24

Information Ratio Calculation

Answer 24

(Average ROR - Benchmark ROR) / Standard deviation of the excess return during a given period

Question 25

Two Types of Indices

Answer 25

Price-weighted index

Market Capitalization-weighted index

Question 26

How is the DJIA computed?

Answer 26

The 30 stock prices are added up and then divided by an adjusted divisor.

Question 27

DJIA Shortcomings

Answer 27

Fails to reflect payment of cash dividends, ignores stock dividends of less than 10%, and consists of a biased sample of stocks

Question 28

SP500 Computation

Answer 28

Summing the market capitalization value of the 500 companies, dividing by the base year value and then multiplying this amount by 10

Question 29

SP500

Answer 29

Benchmark for US Large-cap equity investments and is composed of industrial stocks, transportation stocks, utilities, and financial institutions

Question 30

Russell 2000

Answer 30

Used to benchmark small cap companies. A subset of the Russell 3000 index, which represents most US equities

Question 31

MSCI EAFE Index

Answer 31

was created as a measure of the international securities markets. Provides an indiciation of how a portfolio consisting of companies outside of the US might perform over time

Question 32

Wilshire 5000 Index

Answer 32

Consists of over 5,000 US based companies and is often used as a measure of the overall market within the US

Question 33

JP Morgan indices

Answer 33

track emerging markets, government debt, and corporate asset classes

Question 34

Test Tip: Benchmarking

Answer 34

You should strive to make as accurate a comparison as possible when comparing a portfolio against a benchmark. This normally entails coming up with a blended benchmark.

Question 35

Current Yield Calculation

Answer 35

Annual Interest Rate/Current Market Price

Question 36

Yield to Maturity Calculation

Answer 36

PV = current market price of bond 
FV= Face Value of the Bond 
PMT = interest rate * face value / 2
N = number of years * 2, aka number of periods

Question 37

Yield to Call Calculations

Answer 37

Same calculation as YTM except that the par value of the bond is replaced by the call value, and the number of years is replaced by the first potential call date

Question 38

Taxable Equivalent Yield (TEY) (Federal Tax Free Only)

Answer 38

Tax-exempt yield / 1 - Marginal Tax Rate

Question 39

TEY for double tax-exempt

Answer 39

(tax-free equivalent yield) / 1 - (FMTB + SMTB(1-FMTB))