Question

3. Assume many stocks in the market, two of which have the following characteristics: Expected Return (%) 10 15 Standard Deviation (%) | 10 Stock A Stock B 20 Stocks A and B are perfectly negatively correlated (correlation = -1). What is the market risk-free rate? (hint: how can you construct a risk-free portfolio?)

Answer 1

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ke - Microsoft Excel (Product Activation Failed) Add-Ins File Home Insert Page Layout Formulas Data Review View - 2x % Cut AutoSum - A Dr General Calibri -11AA = = = BI U DA * Wrap Text Merge Merge & Center Center SF 4:0 .00 8.9 Insert Delete Format E Copy Paste Format Painter Clipboard UC39 $ - % % Number Conditional Format Formatting as Table Styles Fill Clear Cell Styles Sort & Filter Editing Find & Select Font Alignment Cells TU UC UD UE 31 32 36 37 38 39 40 41 42 43 44 TV TW TX TY TZ UA UB Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio in equilibrium will always be the risk-free rate To find the proportions of this portfolio: Lets assume : WA invested in Stock A, WB= (1-WA) invested in Stock B we have to take standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation reduces to: OP= ABS[WAOA-WBOB] 0 = WA(0.10)-(1-WA)(0.20) 0 = 0.10 WA-0.20 +0.20 WA 0.6667 = (WA) WA= 0.6667 wB= 0.3333 The expected rate of return on this risk-free portfolio is: E(r) = (0.6667 x 0.10) + (0.3333 * 0.15) = 11.67% Therefore, the risk-free rate must also be 11.67% answer 48 49 50 convexity DGM betaport future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean O HIM Rea KE CAPM UTILITY, SHARPE, beta ferences: AG470 YIELD bond portfolio WACC BOJ 120% - RI O B A .lll TO 25-11-2019

- 2x Find & Select UF ke - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-ins % Cut Σ AutoSum : A Calibri -11AA = = = Dr Wrap Text General Ea Copy Fill Paste B U I B- A Merge & Center - $ -% Sort & Format Painter . Formatting as Table Styles 2 Clear Filter Clipboard Font Alignment Number Styles Cells Editing TX122 - fx TU TV TW T X TY TZ UA UB UC UD 109 110 111 112 113 NOTE 114 WE CAN ALSO VERIFY BY CHECKING THAT STANDARD DEVIATION = RISK = 0 115 116 PORTFOLIO SD = SQRT (WA)^2* (SDA)^2 + (WB)^2* (SDB)^2 + 2 WA*WB*(SDA)*SDB)*rAB) 117 PORTFOLIO SD = sqrt [((66.6667%)^2*(10%)^2 + (33.3333%)^2*(20%)^2 + 2*(66.6667%)*(33.3333%)*(10%)*(20%)*(-1))] 118 PORTFOLIO SD = 0.0000000 119 120 IT IS COMING ZERO. SO ANSWER IS CORRECT 121 122 123 124 125 126 127 Convexity DGM betaport future INDEX INTL CAP BUD SANDRINE LEASING PV, FV, ANNUITY DIR right clean NEM Rea KE CAPM UTILITY, SHARPE, beta ferences: AG470 YIELD bond portfolio WACC RO BO! 120% - -_ + 9 * * *0 ENG 25-11-2019 2. B