Question

In: Statistics and Probability

You are considering two investments. Let X represent the proportional rate of return on the first...

You are considering two investments. Let X represent the proportional rate of return on the first investment, and let Y represent the proportional rate of return on the second investment. These are annual rates of return.

X is approximately normally distributed with mean 0.25 and standard deviation 0.2. Y is approximately normally distributed with mean 0.30 and standard deviation 0.4.

The first six questions are about the rates of return, X and Y.

What is the probability of a negative rate of return on the first investment?  

What is the probability of a negative rate of return on the second investment?  

If the rates of return on these investments are independent, what is the probability that the rates of return on both investments will be negative?

What is the expected amount by which Y exceeds X? HINT: The amount by which the rate of return on the second investment is higher than the rate of return on the first investment is Y - X.   

If the rates of return on these investments are independent, what is the probability that the second investment will have a higher rate of return than the first? HINT: Restate the question in terms of the rate of return on the second investment minus the rate of return on the first investment.  

If instead X and Y have a correlation of – 0.4 (a negative correlation), what is the probability that the second investment will have a higher rate of return than the first? HINT: Be careful! You’re given the correlation, not the covariance!  

The remaining questions are about the value of your portfolio after one year (the dollar amount you end up with), taking into account both the amount you invest and the yield, which depends on the rate of return. For example, if you invest $100, and the proportional rate of return is X, the yield is $100X, and you end up with $100 + $100X.

You have $100 to invest. Suppose you invest $100 in the first investment. What is the expected dollar amount you will end up with? (What is the expected value of your portfolio?)

What is the standard deviation of the dollar amount you will end up with?

What is the probability you will end up with less than $80?    

Alternatively suppose you invest $100 in the second investment. What is the probability you will end up with less than $80?  

Suppose you invest $30 in the first investment and $70 in the second investment. What is the expected dollar amount you will end up with?  

If X and Y are independent, what is the standard deviation of the dollar amount you will end up with?  

What is the probability you will end up with less than $80?  

Suppose instead that X and Y have a correlation of – 0.4 (a negative correlation). You invest $30 in the first investment and $70 in the second investment. What is the standard deviation of the dollar amount you will end up with?  

What is the probability you will end up with less than $80?  

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

You are considering two investments. Let X represent the proportional rate of return on the first...
You are considering two investments. Let X represent the proportional rate of return on the first investment, and let Y represent the proportional rate of return on the second investment. These are annual rates of return. X is approximately normally distributed with mean 0.35 and standard deviation 0.3. Y is approximately normally distributed with mean 0.40 and standard deviation 0.5. These six questions are about the rates of return, X and Y. 1. What is the probability of a negative...
Internal Rate of Return Manzer Enterprises is considering two independent investments:     A new automated materials handling...
Internal Rate of Return Manzer Enterprises is considering two independent investments:     A new automated materials handling system that costs $900,000 and will produce net cash inflows of $300,000 at the end of each year for the next four years.     A computer-aided manufacturing system that costs $775,000 and will produce labor savings of $400,000 and $500,000 at the end of the first year and second year, respectively. Manzer has a cost of capital of 8 percent. The present value tables provided...
Internal Rate of Return Manzer Enterprises is considering two independent investments: A new automated materials handling...
Internal Rate of Return Manzer Enterprises is considering two independent investments: A new automated materials handling system that costs $900,000 and will produce net cash inflows of $300,000 at the end of each year for the next four years. A computer-aided manufacturing system that costs $775,000 and will produce labor savings of $400,000 and $500,000 at the end of the first year and second year, respectively. Manzer has a cost of capital of 8 percent. The present value tables provided...
Internal Rate of Return Method—Two Projects Munch N’ Crunch Snack Company is considering two possible investments:...
Internal Rate of Return Method—Two Projects Munch N’ Crunch Snack Company is considering two possible investments: a delivery truck or a bagging machine. The delivery truck would cost $48,601.8 and could be used to deliver an additional 54,000 bags of pretzels per year. Each bag of pretzels can be sold for a contribution margin of $0.38. The delivery truck operating expenses, excluding depreciation, are $0.52 per mile for 18,000 miles per year. The bagging machine would replace an old bagging...
You are considering three investments. The first is a bond that is selling in the market...
You are considering three investments. The first is a bond that is selling in the market at $1,200. The bond has a $1,000 par value, pays interest semi-annually at 10%, and is scheduled to mature in 10 years. For bonds of this risk class you believe that a 12% rate of return should be required. The second investment that you are analysing is a preference share ($100 par value) that sells for $95 and pays an annual dividend of $10....
You are considering three investments. The first is a bond that is selling in the market...
You are considering three investments. The first is a bond that is selling in the market at $1 200. The bond has a $1 000 par value, pays interest at 8% and is scheduled to mature in 10 years. For bonds of this risk class you believe that a 9% rate of return should be required. The second investment that you are analyzing is a preferred stock ($125 par value) that sells for $120 and pays an annual dividend of...
Two fair dices, X and Y , are tossed separately. Let A, B and C represent...
Two fair dices, X and Y , are tossed separately. Let A, B and C represent the following three events. A: You got an odd number from die X. B: You got an even number from die Y . C: The sum of two dice is an odd number. Whether A, B, C are independent? Explain!
Patterson Company is considering two competing investments. The first is for a standard piece of production...
Patterson Company is considering two competing investments. The first is for a standard piece of production equipment. The second is for computer-aided manufacturing (CAM) equipment. The investment and after-tax operating cash flows are as follows: Year Standard equipment CAM equipment R R 0 5 000 000 20 000 000 1 3 000 000 1 000 000 2 2 000 000 2 000 000 3 1 000 000 3 000 000 4 1 000 000 4 000 000 5 1 000...
The average rate of return on investments in large stocks has outpaced that on investments in...
The average rate of return on investments in large stocks has outpaced that on investments in Treasury bills by about 7% since 1926. Why, then, does anyone invest in Treasury bills?
You are considering for a client 3 investments as highlighted below. The first a stock, the...
You are considering for a client 3 investments as highlighted below. The first a stock, the second is a long-term corporate bond, and the third is a T-bill. R(expected) Std Dev T-Bill 8% Bond 12% 12% Stock 21% 25% Correlation between S & B .15 a) what is the investment proportions in the minimum variance portfolio of the two risky funds, what is the expected return and standard deviation of that portfolio? b) Draw the investment opportunity set highlighting the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT