Cheat Sheet 371-Final2 - e Lecture 1 2 st dev of average excess return is Realized return historical Growing Annuity PV = C 1 g 1 r g 1 r e)=(R(R N

# 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 is σ ( ´ R e ) = σ ( R e ) N ; Expected return: forward-looking, Realized return: historical Growing Annuity PV = C r g [ 1 ( 1 + g 1 + r ) t ] ; effectiverateused ¿ discount dependson frequency of CFs // EARr 1 = e APR 1 P 0 = C ( 1 + r ) + C + F ( 1 + r ) 2 → P 0 ( 1 + r ) 2 = C ( 1 + r ) + C + F →P 0 ( 1 + 2 r + r 2 ) = C + Cr + C + F→ P 0 ( r 2 ) + ( 2 P 0 C ) r + ( P 0 2 C F ) = 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): 1 d T ¿ 1 T 1 d t = 1 ( 1 + r t ) t ;r T = ¿ // Taylor rule: Fed fundsr = 1.5 π + 0.5 ^ y ; y is % dev of output from trend real GDP, inf. over preced. 4 quarters Market value of replicating portfolio (no arbitrage): sum of cash flow as a % of bond x price of bond. Spot rates that will prevail in the future are unknown as of today  Bootstrapping is a procedure to obtain spot rates from the prices of coupon bonds: 1 + r 1,2 e 2 ¿ 2 1 + r 2,0 2 ¿ 2 ¿ 2 ¿ ¿ 1 + r 3,0 2 ¿ 2 ¿ 3 = ¿ ¿ 1 + r 2,0 ¿ 2 ( 1 + r 1,2 e ) ;semi annual ¿ 1 + r 3,0 ¿ 3 = ¿ ¿ Lecture 4 (Valuation of Fixed Income Securities II): Lecture 4 (FI Securities II): Slope of the PP increases with maturity for zero coupon bonds. Slope of the PP decreases with coupon rate Macaulay D = t = 1 T w t t = 1 + r r ( 1 + r ) + T ( c r ) c [ ( 1 + r ) T 1 ] + r ( constant c ) ; w t = c ( 1 + r ) t 1 P ;w T = 100 + c ( 1 + r ) T 1 P ; PV ( CF ) A coupon bond has the same interest rate sensitivity as a zero-coupon bond of maturity equal to that duration. Weights becomes less, care less into the distant future. •D generally increases with time to maturity (but not always) •D always decreases with coupon rate •D of a portfolio of two bonds with the same YTM is the value weighted average of the duration of the individual bonds.