# Cheat Sheet 371-Final2 - e Lecture 1 & 2: st dev of average...

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Lecture 1 & 2:st dev of average excess return isσ(´Re)=σ(Re)N; Expected return: forward-looking,Realized return: historicalGrowing Annuity PV=Crg[1(1+g1+r)t]; effectiverateused¿discount dependson frequency of CFs//EARr1=eAPR1P0=C(1+r)+C+F(1+r)2→ P0(1+r)2=C(1+r)+C+F →P0(1+2r+r2)=C+Cr+C+F→ P0(r2)+(2P0C)r+(P02CF)=0;r=One nominal dollar received next year is 1/(1+π) real dollars, where π is the inflation rate during the year:1+r (real) = (1+i)/(1+pi)Lecture 3 (Valuation of Fixed Income Securities I):1dT¿1T1dt=1(1+rt)t;rT=¿//Taylor rule:Fed fundsr=1.5π+0.5^y; y is % dev of output from trend real GDP, inf.over preced. 4 quartersMarket value of replicating portfolio (no arbitrage): sum of cash flow as a % of bond x price of bond. Spotrates that will prevail in the future are unknown as of today  Bootstrapping is a procedure to obtain spotrates from the prices of coupon bonds:1+r1,2e2¿21+r2,02¿2¿2¿¿1+r3,02¿2¿3=¿¿1+r2,0¿2(1+r1,2e);semiannual¿1+r3,0¿3=¿¿Lecture 4 (Valuation of Fixed Income Securities II):Lecture 4 (FI Securities II):Slope of the PPincreases with maturity for zero coupon bonds. Slope of the PP decreases with coupon rateMacaulay D=t=1Twtt=1+rr(1+r)+T(cr)c[(1+r)T1]+r(constant c); wt=c(1+r)t1P;wT=100+c(1+r)T1P; PV(CF)A coupon bond has the same interest rate sensitivity as a zero-coupon bond of maturity equal to thatduration. Weights becomes less, care less into the distant future. •D generally increases with time tomaturity (but not always) •D always decreases with coupon rate •D of a portfolio of two bonds with thesame YTMis the value weighted average of the duration of the individual bonds.

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