r_t = (MV_t - MV_(t-1))/(MV_(t-1))
If CF occurs BOP t: (MV_t - (MV_(t-1) + CF_t))/(MV_(t-1) + CF_t)
If CF occurs EOP t: ((MV_t - CF_t) - MV_(t-1))/(MV_(t-1))
Total rate of return - answer-Includes realized and unrealized capital gains in addition to income
-Allows return to be compared ac...
If CF occurs EOP t: ((MV_t - CF_t) - MV_(t-1))/(MV_(t-1))
Total rate of return - answer-Includes realized and unrealized capital gains in
addition to income
-Allows return to be compared across different types of investments
-Became more popular after the 1960s
*Higher asset volatility
*Higher investor sophistication
*Greater computing power
time-weighted rate of return - answer-TWR = compound growth rate of $1 initially
invested in the account
Musst be calculated every time an external CF occurs
Divide total period t into n sub-periods between external CFs (i = 1, 2, ..., n)
r_(t,i) = (MV_i - CF_i) - MV_(i-1))/(MV_(i-1))
Chain-link the sup-period returns (r_(t,i))
TWR = Product of (1+ r_(t,i) - 1)
1 + r_(t,1) = "wealth relative" for sub-period 1, etc.
money-weighted rate of return - answer-MWR = average compound growth rate of
all money invested in an account (IRR)
There is usually not a closed form solution for R (must be solved for iteratively)
TWR vs MWR - answer-Offsetting advantages and disadvantages
,Sensitive to size and timing of CFs: TWR-no MWR-yes
Calculation freq required: TWR-High MWR-Low
Admin expense and potential for error: TWR-High, MWR-Low
Appropriate if manager has little/no control over external CFs: TWR-Yes, MWR-No
MWR will diverge from TWR if there are large external CFs and/or high volatility
Linked internal RAte of Return (LIRR) - answer-Blends advantages of TWR and MWR:
1.) Calculate MWR over reasonably frequent time intervals
2.) Chain-link the MWRs over the entire evaluation period
LIRR is an acceptable proxy for TWR unless there are unusual circumstances
-Unusual = large external CFs (10%+ of AV) an/or volatile account growth
-Conclusion is based on a BAI study of monthly valuations and daily CFs
Annualized Return - answer-Known as compound growth rate or geometric mean
Data Quality Issues - answer-Reported rates of return are only as accurate as their
inputs
-Liquid, transparently priced securities have the most reliable returns
-Thinly traded securities - could use matrix pricing
*Estimate prices using dealer quoted prices for similar securities
-Highly illiquid securities - carry at cost or price at last trade
Report on a trade-date, fully accrued bases
-Reflect impact of unsettled trades and income owed but not paid
Current Yield - answer-only measures coupon income
Current Yield = Annual Dollar Coupon Interest / Price
Yield To Maturity - answer-IRR such that PV (CFs) = Price (or Initial Investment)
-Typically expressed on a BEY basis (nominal semiannual)
-Portfolio IRR can be calculated by combining all bond cash flows
Yield to Call - answer-Like YTM but using a call date instead of maturity date
Yield if bond is held until called at either
1.) First call date - date at which the bond can be called
2.) First par call date - date at which the bond can be called at par
Total Return - answer-rate that accumulates full price and coupons to projected
total future dollars at end of horizon
Semiannual Total Return = (Total Future Dollars/Full Price of Bond)^(1/n) - 1
n = # of semiannual periods
Yield Measures Compared - answer-Sources of bond return:
, 1.) Coupon interest: Current Yield-Yes, YTM/YTC-Yes, Total Return-Yes
2.) Capital Gain or loss: Current Yield-No, YTM/YTC-Yes, Total Return-Yes
3.) Interest-on-interest: Current Yield-No, YTM/YTC-Yes, but at YTM/YTC, Total
Return-Yes
None of the "conventional" yield measures accurately reflect all 3 sources.
Interest-on-interest can be very significant (up to 80% of total return)
Significance of Interest-On-Interest - answer--Can be very significant (up to 80% of
return)
-If reinvestment rates are less than YTM or YTC, total return <YTM or YTC
-Characteristics that increase exposure to reinvestment risk:
*Longer maturity dates
*Higher coupons
-Zero coupon bonds have no reinvestment risk if held to maturity
Relationship Among Coupon, Current Yield, and YTM - answer-Bond Selling at:
Relationship:
Par coupon rate = Current yield =YTM
Discount coupon rate < current yield < YTM
Premium coupon rate > current yield > YTM
"Discount" means the price < Par; "premium" is the opposite
Yield-to-worst - answer-lowest possible YTC for any possible future call date
-most conservative measure for a callable bond
Problems with Yield to Call - answer-Problems in common with YTM
1.) Assumes coupons reinvested at YTC
2.) Assumes investor will hold bond to assumed call date
Additional problems:
1.) Can't reflect reinvestment of proceeds at call date
2.) Assumes the issuer actually calls bond at call dates
Floating Rate Bonds - answer-coupon fluctuates with reference rate R_t
Coupon_t = (R_t + Spread) * Par
Therefore, coupon values are unknown
Discount margin - answer-estimated average spread over the reference rate for the
life of the security
Determining the Discount Margin - answer-Bond Selling at: Relationship
Par Discount Margin = spread over ref rate
Discount Discount margin > spread over ref rate
Premium Discount Margin < spread over ref rate
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