Measures of Investment Returns Flashcards
What is the compound return on $100 over the following 10%, 5%, 8%. What is the average geometric return? What is the arithmetic average return?
Geometric = (1.1)(1.05)(1.08) 24.74/ 3 = 8.24
Arithmetic = 1.1+1.05+1.08/3 = 1.076 = 7.67%
Returns that compound are also called what
Geometric
Geometric uses multiplication whereas arithmetic uses
addition
Dollar weighted return
actual dollar return returns experienced by investors who add or withdraw investment funds over time
Dollar weighted return is the same thing as
IRR
IRR gives you what rate on invested cash
the true annualized compounded rate of return. How much money was made/lost on ALL monies invested
Buy a stock for $10, sell it in 3 years for $12, pay pays $.33 a year in dividends. What is the IRR?
PV = 10 CHS
FV = 12
PMT = .33
N = 3
I = 9.38%
You buy 2 shares of a stock for $10 that pays $.33 dividend. At the end of year 1 you add 10 more shares at $11 and then sell at $12 the end of year 3. What is the IRR
C0 = -20
C01 = 10 * 11 = -110 plus .33 dividend from 2 shares = .66 + -110 = 109.34
C02 = 12 * .33 = 3.96
C03 = 3.96 + 12 * 12 = 147.96
20 CHS g CF0
109.34 CHS g CFj
3.96 g CFj
147.96 g CFj
f IRR
7.8372 or 7.84
Time Weighted Rate of Return
Geometric average return of individual holding period returns HPR
= How much money was made or lost for each dollar invested
CAGR Cumulative Annual Growth Rate
Annual compounded rate of return. Rate at which a lump sum, invested in an investment strategy at the beginning with no additions or subtractions, would have grown on average each year
Risk Adjusted Return
investment returns which are modified by the level of risk taken to achieve the returns. When comparing 2 securities, need to adjust for risk so apples to apples comp can be made. Adjusted using standard deviation and beta. Coefficient of Deviation is a risk adjusted return.
Holding Period Return
measurement expressed as a percent of return or loss, realized or expected, on an investment during a single period, usually one year
3 Common ways returns are calculated over multiple periods
Arithmetic Avg/Mean Return = simple return
Dollar Weighted Return = IRR
Geometric Avg Rate of Return = Time Weighted Return
Key reinvestment assumption on YTM
interest payments are reinvested at the YTM rate
Yield To Maturity definition
IIR of a bond, which is yield earned on a bond from the time acquired to maturity date
Yield to Call definition
IRR of a bond assuming it will be called, yield from when you acquire to when its called
What is the current yield on a bond with a $100 coupon currently priced at $952?
100/952 = .105 = 10.5%
What is the YTM on a bond with a $100 coupon priced at $952? Matures in 3 years?
Solve for I
PV = 952 CHS
PMT = 50 (100/2)
N = 6 (3 *2)
FV = 1000
I = 5.98 YOU NEED TO MULTIPLY BY 2
11.96%
Current yield > YTM when bond price is
at a premium
YTM > current yield when bond price is
at a discount
Premium does what to YTM
reduces
Discount does what to YTM
increases
Does current yield consider premium or discount?
No
When should you buy bonds? When interest rates are going to do what
go down
What should you do to your bond maturities if you expect rates to increase?
shorten maturities
When doing yield to call you do the same as YTM but adjust what
-use call date instead of maturity date
-principal + call penalty for principal repayment
A call on a callable bond would most likely occur when rates have done what
call would occur after rates have declined
Tax Equivalent Yield refers to what bonds
must convert the municipal yield to Taxable Equivalent Yield
Compare 10% taxable bond to 7.5% tax exempt bond for someone in the 28% tax marginal bracket
.75 / (1-.28) = 10.42% TEY is better than 10%
A rational investor wants to achieve what type of return regarding risk?
The maximum return for the units of risk taken
Sharpe Ratio is what type of risk adjusted return return
total risk adjusted return
Treynor is what type of risk adjusted return
Systematic risk adjusted return
Capitalized earnings are the cap on the rate
earnings
————
required rate
