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An investor wants t0 invest S80,000 in two mutual funds, A and B. The rates of return; risks and minimum investment requirements for each fund are:FundRate of retur...

Question

An investor wants t0 invest S80,000 in two mutual funds, A and B. The rates of return; risks and minimum investment requirements for each fund are:FundRate of returnRiskMinimum investment S30,000 S20,00014 % 11 %0.6 0.4Note that a low risk rating means a less risky investment: The investor wants to maximize the expected rate of return while minimizing her risk. Any money beyond the minimum investment requirements must be invested in one of the funds (all S80,000 have to be invested) Assume that

An investor wants t0 invest S80,000 in two mutual funds, A and B. The rates of return; risks and minimum investment requirements for each fund are: Fund Rate of return Risk Minimum investment S30,000 S20,000 14 % 11 % 0.6 0.4 Note that a low risk rating means a less risky investment: The investor wants to maximize the expected rate of return while minimizing her risk. Any money beyond the minimum investment requirements must be invested in one of the funds (all S80,000 have to be invested) Assume that the risk of a portfolio is equal to the weighted average of the risks of the individual funds Find the investment policy that maximizes return_ What is the risk and return under this policy? Find the investment policy that minimizes risk What is the risk and return under this policy? Formulate a goal programming model with a MINIMAX objective function_ Assume that maximizing return and minimizing risk are equally important:



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A popular theory in investment states that you should invest a certain amount of money in foreign investments to reduce your risk. The risk of a portfolio is defined as the standard deviation of the rate of return. Refer to the graph on the following page, which depicts the relation between risk (standard deviation of rate of return) and reward (mean rate of return). (a) Determine the average annual return and level of risk in a portfolio that is $10 \%$ foreign. (b) Determine the percentage that should be invested in foreign stocks to best minimize risk. (c) Why do you think risk initially decreases as the percent of foreign investments increases? (d) A portfolio that is $30 \%$ foreign and $70 \%$ American has a mean rate of return of about $15.8 \%,$ with a standard deviation of $14.3 \% .$ According to Chebyshev's Inequality, at least $75 \%$ of returns will be between what values? According to Chebyshev's Inequality, at least $88.9 \%$ of returns will be between what two values? Should an investor be surprised if she has a negative rate of return? Why?

So for this problem we um are looking at a mutual fund company that charges a fee. Um And we see the different charges for the assets in the fund. We want to let X. To note the fee the company charges as a percentage. And we're going to express a vector as a linear function. So we're going to have the point Is going to be the feast of .47. And then the corresponding amount is 41 billion. And then when it's 0.18 B 300 billion. So we can find the linear function by comparing the slope of 300 -41, divided by 4.47 minus 0.18. So we see this is going to be the slope and then we will find the Y intercept simply by considering the fact that Um this is actually gonna be easier .18 minus this. So this will actually be a negative value. So you see it's decreasing as the percentage increases. So what we'll do is we'll find our revenue function based on this And then we're given the cost function. So this is now a problem 46. The cost function is given to us as a negative 2.5 x plus one. Which then tells us that the um we want to find the value of X. That maximize profit. So we remember that profit is equal to revenue minus cost. Then all we have to do is differentiate this so take p prime of X and find where it reaches that maximum value

Mhm. Wow. When a mutual fund company charges a fee of .47% on its index funds, Its assets and the funds are 41 billion. And when it charges 80 or 18%,, The assets in the fund, or 300 billion. So we want to express FX is a linear function. So in order to do that, we would have a being the assets. So we'll have the point 0.47, that's the percentage. And the corresponding assets are 41 billion. And then we'll have um Your .18 And the corresponding assets are 300 million. So we're going to create a linear function from that. So it's been 300 -41 Divided by 0.18 Your plane for seven. It's been up. Get any negative 893. Uh as our linear function, we could use that as the slope. And we can also plug in a point here to find the y intercept.


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