Question
Prove that there is an arbitrage opportunity and show how you would go to exploit it (using calculation). Find the highest amount of profit you
Prove that there is an arbitrage opportunity and show how you would go to exploit it (using calculation).
Find the highest amount of profit you can make on an arbitrage play that equals $1,000,000.
3 portfolios: rf is 4%
A: beta is 0.5 and expected return is 7%
B: beta is 1.1 and expected return is 11.7%
C: beta is 1.25 and expected return is 11.5%
Step by Step Solution
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Step: 1
To prove an arbitrage opportunity we need to find a combination of portfolios that offers a riskfree profit In this case we can exploit the differences in expected returns and betas across portfolios to create such an opportunity Lets assume we have 1000000 to invest We will construct a portfolio by investing in each of the three portfolios A B and C in such a way that the total beta of our portfolio is zero effectively making it a riskfree portfolio This is achieved by adjusting the weights of each portfolio based on their betas Given Riskfree rate rf 4 Expected returns and betas of each portfolio Portfolio A Expected return ER 7 Beta 05 Portfolio B Expected return ER 117 Beta 11 Portfolio C Expected return ER 115 Beta 125 To create a riskfree portfolio we need to solve for the weights w of each portfolio such that the weighted sum of betas is zero wAbetaA wBbetaB wCbetaC 0 Lets denote the weights of portfolios A B and C as wA wB and wC respectively We also want to maximize the expected return of our riskfree portfolio which is the weighted sum of the expected returns of each portfolio ER wAERA wBERB wCERC To find the weights that maximize the expected return of the riskfree portfolio while keeping the total beta zero we can solve these equations simultaneously Lets denote the weights of each portfolio as follows wA x wB y wC 1 x y since the total weight of all portfolios must sum to 1 Now we can solve for x and y using the equations 1 x05 y11 1 x y125 0 equation for total beta 2 ER x7 y117 1 x y115 equation for expected return After solving this system of equations we will obtain the optimal weights x and y that maximize the expected return while keeping the total beta zero Once we have the optimal weights we can calculate the maximum profit we can make on the arbitrage play The profit will be the difference ...
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Organic Chemistry
Authors: L. G. Wade Jr.
8th edition
321768418, 978-0321768414
