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  • 1 Post By HallsofIvy
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March 26th, 2014, 02:55 AM   #1
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Please explain this solution

The riskiness of a portfolio, S, is a function of the percent of the portfolio comprised of equity, E where S = 0.02 + 0.2E. In turn the percent of Equity,E,is determined by the desired rate of return, R where E=8R - 0.48. Complete the chain rule calculation required to determine the trade-off between risks and returns.


Part 2 Given the formula you created using the chain rule, where S = 0.02 + 0.2E and R=0.06 + 0.125E, insert the values and calculate the relationship between change in risk and change in return.

DS/DR = ?

Answer is 1.6 please explain
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March 26th, 2014, 05:53 AM   #2
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Re: Please explain this solution

The "derivative of f at a given point" can be defined as "the slope of the tangent line to the graph of y= f(x) at that point". For linear functions, like these the "tangent line" is just the line itself and the "slope of the tangent line" is just the slope of the line.

You are given that S = 0.02 + 0.2E so that dS/dE= 0.2
You are given that E=8R - 0.48 so dE/dR= 8. Using the chain rule, as you wrote it, dS/dR= (dS/dE)(dE/dR)= (0.2)(= 1.6.

For simple, linear equations like this, you don't really need the chain rule. Since S= 0.02+ 0.2E and E= 8R- 0.48, S= 0.02+ 0.2(8R- 0.4= 0.02+ 1.6R- 0.096= 1.6- 0.076. That is a linear equation and so its slope, and so derivative, dS/dR, is 1.6.
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