# cheat sheet

Effective annual rate on a three-month T-bill: Optimal capital allocation: Y= E(rp)- Rf / A(std)^2portfilio – 1 = (1.02412)4 – 1 = 0.1000 = 10%

Effective annual interest rate on coupon bond paying 5% semiannually: (1 + 0.05)2 – 1 = 0.1025 = 10.25%

The effective annual yield on the semiannual coupon bonds is (1.04)2 -1 = 8.16%. after tax yield = (taxable yield)*(1-tax rate) Holding period return =

Price of a Zero-Coupon Bond =

Bond Equivalent YTM = Semi-annual YTM 2

The bond is selling at par value. Its yield to maturity equals the coupon rate, 10%. If the first-year coupon is reinvested at an interest rate of r percent, then total proceeds at the end of the second year will be: [100 (1 + r) + 1100]. Therefore, realized compound yield to maturity will be a function of r as given in the following table: r

Total proceeds

Realized YTM = = 1

8%

$1,208

– 1 = 0.0991 = 9.91%

10%

$1,210

– 1 = 0.1000 = 10.00%

12%

$1,212

– 1 = 0.1009 = 10.09%

HPR =

Time-weighted average returns are based on year-by-year rates of return. Portfolio= (1-y)(risk free) + (y)(equity index)

Year

Return = [(Capital gains + Dividend)/Price]

2010-2011

(110 – 100 + 4)/100 = 0.14 or 14.00%

2011-2012

(90 – 110 + 4)/110 = –0.1455 or –14.55%

2012-2013

(95 – 90 + 4)/90 = 0.10 or 10.00%

Arithmetic mean: [0.14 + (–0.1455) + 0.10]/3 = 0.0315 or 3.15% Geometric mean: – 1

= 0.0233 or 2.33%

Given that A = 4 and the projected standard deviation of the market return = 20%, we can use the below equation to solve for the expected market risk premium: A = 4 = =

E(rM) – rf = AM2 = 4 (0.20) = 0.16 or 16%

The...

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