Module 7: Measures of Investment Returns Flashcards
Simple Rate of Return
Divide the total return by the number of years that the investor has held the asset
Compound Rate of Return
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
Arithmetic Mean
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.
Geometric Mean
Assumes compounding returns. Use calculator:
PV: -1
FV: (1+return year 1)*(1+return year 2)…
N: number of periods
Solve for I/YR
Geometric vs. Arithmetic Mean
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
Time-Weighted Return
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)
Dollar-Weighted Approach
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.
Nominal Rate of Return
It’s stated rate of return for a given period without accounting for invlation.
Real Rate of Return
Takes into account inlation:
((1+Rn)/(1+inflation)-1) * 100
Rn = Absolute Return
After-Tax Inflation-Adjusted Rate of Return
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.
Annual Percentage Rate
The yearly cost of funds expressed as a percentage. However, the nominal APR does not take compounding into consideration.
Effective Annual Rate
The annual precentage rate taking into consideration the impact of compounding.
(1+(i/n))^n -1
i = annual interest rate n = number of peiods
Total Return
Includes the income from dividends or interest plus any capital appreciation over a given time period.
SEC Yield
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.
Holding Period Return
“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
Risk-Adjusted Return
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
Jensen’s Alpha
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.
Jensen’s Alpha Calculation
Average rate of return for portfolio P - (risk free ROR + (market’s ROR - RFROR)*Beta for Portfolio P)
Treynor Ratio
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
Treynor Ratio Calcuation
(average ROR-RFROR)/ Beta for portfolio P
Sharpe Ratio
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
Sharpe Ratio Calculation
(average ROR - RFROR) / St. Dev
Information Ratio
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
Information Ratio Calculation
(Average ROR - Benchmark ROR) / Standard deviation of the excess return during a given period
Two Types of Indices
Price-weighted index
Market Capitalization-weighted index
How is the DJIA computed?
The 30 stock prices are added up and then divided by an adjusted divisor.
DJIA Shortcomings
Fails to reflect payment of cash dividends, ignores stock dividends of less than 10%, and consists of a biased sample of stocks
SP500 Computation
Summing the market capitalization value of the 500 companies, dividing by the base year value and then multiplying this amount by 10
SP500
Benchmark for US Large-cap equity investments and is composed of industrial stocks, transportation stocks, utilities, and financial institutions
Russell 2000
Used to benchmark small cap companies. A subset of the Russell 3000 index, which represents most US equities
MSCI EAFE Index
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
Wilshire 5000 Index
Consists of over 5,000 US based companies and is often used as a measure of the overall market within the US
JP Morgan indices
track emerging markets, government debt, and corporate asset classes
Test Tip: Benchmarking
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.
Current Yield Calculation
Annual Interest Rate/Current Market Price
Yield to Maturity Calculation
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
Yield to Call Calculations
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
Taxable Equivalent Yield (TEY) (Federal Tax Free Only)
Tax-exempt yield / 1 - Marginal Tax Rate
TEY for double tax-exempt
(tax-free equivalent yield) / 1 - (FMTB + SMTB(1-FMTB))
