ms3034_2026T1_Q2_NA.pdf

A two-asset portfolio consists of 30% in Asset 1 ( [[IMAGE:e003f9bf246aced9_2_2]] , and [[IMAGE:e003f9bf246aced9_2_3]] ) and 70% in Asset 2 ( [[IMAGE:e003f9bf246aced9_2_4]] , and [[IMAGE:e003f9bf246aced9_2_5]] ). If the covariance between Asset 1 and Asset 2 is 0.1, then what is the expected return of the portfolio? (Note: [[IMAGE:e003f9bf246aced9_2_6]] represents the expected rate of return and [[IMAGE:e003f9bf246aced9_2_7]] represents the standard deviation of the rate of return, respectively, for an asset [[IMAGE:e003f9bf246aced9_2_8]] .)

An equally weighted portfolio of 100 uncorrelated assets, each with a standard deviation of return [[IMAGE:e003f9bf246aced9_2_9]] %, has a portfolio standard deviation of

If the slope of the Capital Allocation Line (CAL) is 0.5 and the risk-free rate is 4%, what is the expected return of a portfolio on the CAL with a standard deviation of 12%?

An individual with [[IMAGE:e003f9bf246aced9_3_10]] has a wealth of 1,000 units. There is a 10% chance of losing 500 due to an accident. What is the expected utility of this individual?

A risk-neutral investor is offered a bet: 20% chance to win 500, 30% chance to win 200, and 50% chance to lose 100. What is the fair price of this bet?

A risk-neutral lender requires an expected return of 10%. A borrower has a 20% probability of total default (0 recovery). What is the promised interest rate that the lender should charge?

Asset A has [[IMAGE:e003f9bf246aced9_4_11]] % and [[IMAGE:e003f9bf246aced9_4_12]] %. Asset B has [[IMAGE:e003f9bf246aced9_4_13]] % and [[IMAGE:e003f9bf246aced9_4_14]] %. If the correlation between the assets [[IMAGE:e003f9bf246aced9_4_15]] , what is the standard deviation of a portfolio with equal weights? (Note: [[IMAGE:e003f9bf246aced9_4_16]] represents the rate of return and [[IMAGE:e003f9bf246aced9_4_17]] represents the standard deviation of the rate of return.)

What is the Sharpe Ratio for a portfolio with an expected return of 15%, a risk-free rate of 3%, and a standard deviation of 20%?

Given two assets with [[IMAGE:e003f9bf246aced9_4_18]] % and [[IMAGE:e003f9bf246aced9_4_19]] % and correlation [[IMAGE:e003f9bf246aced9_4_20]] . What is the weight of Asset 1 ( [[IMAGE:e003f9bf246aced9_4_21]] ) that results in a zero-variance portfolio? (Note: [[IMAGE:e003f9bf246aced9_4_22]] represents the standard deviation of the rate of return for an Asset [[IMAGE:e003f9bf246aced9_4_23]] )

The risk-free rate is 4%. The optimal risky portfolio has an expected rate of return [[IMAGE:e003f9bf246aced9_5_24]] % and the standard deviation of the portfolio rate of return [[IMAGE:e003f9bf246aced9_5_25]] %. If an investor wants an expected return of 10%, what weight should she put in the risky portfolio?

You short-sell 80 shares of a stock at Rs 60 per share. One year later, you buy them back at Rs 55 per share. Ignoring interest and transaction costs, what is your total profit?

A portfolio has a beta of 1.5. The risk-free rate is 5% and the market risk premium is 8%. According to CAPM, what is the expected return?

The risk-free rate is 4%. The optimal risky portfolio has an expected rate of return [[IMAGE:e003f9bf246aced9_6_26]] % and the standard deviation of the portfolio rate of return [[IMAGE:e003f9bf246aced9_6_27]] %. If an investor invests 60% of his wealth in the optimal risky portfolio and the remaining wealth in a risk-free asset, what will be the standard deviation of the investor’s portfolio?

There are two assets: Asset X ( [[IMAGE:e003f9bf246aced9_6_28]] , [[IMAGE:e003f9bf246aced9_6_29]] ) and Asset Y ( [[IMAGE:e003f9bf246aced9_6_30]] , [[IMAGE:e003f9bf246aced9_6_31]] ). The covariance between the two assets is [[IMAGE:e003f9bf246aced9_6_32]] . What is the Global Minimum Variance (GMV) weight for Asset X for the two-asset portfolio? (Note: [[IMAGE:e003f9bf246aced9_6_33]] represents the expected rate of return and [[IMAGE:e003f9bf246aced9_6_34]] represents the standard deviation of the rate of return, respectively for an asset [[IMAGE:e003f9bf246aced9_6_35]] .)

If an investor's risk aversion coefficient [[IMAGE:e003f9bf246aced9_6_36]] , the risk-free rate is 0.05, and the risky asset has an expected rate of return [[IMAGE:e003f9bf246aced9_6_37]] and the variance of rate of return [[IMAGE:e003f9bf246aced9_6_38]] . Assuming mean-variance preferences ( [[IMAGE:e003f9bf246aced9_6_39]] ), what is the optimal weight ( [[IMAGE:e003f9bf246aced9_6_40]] ) in the risky asset?

A project pays 200 units with probability 0.25, 400 units with probability 0.40 and 600 units with probability 0.35, in the next year. If the expected annual discount rate is 10%, what is the project's present value? (Rounded off to nearest integer)

An asset has a return of 20% in a "Boom" condition (probability 0.3), 8% in a “Normal” condition (probability 0.4) and 2% in a "Bust" condition (probability 0.3). What is the standard deviation of the asset return?

MNO Bank has total assets of Rs 500 billion and a leverage ratio of 5. What is the value of the total liabilities of MNO Bank?

An investor with mean-variance preferences [[IMAGE:e003f9bf246aced9_7_41]] is indifferent between Asset A ( [[IMAGE:e003f9bf246aced9_7_42]] , [[IMAGE:e003f9bf246aced9_7_43]] ) and Asset B ( [[IMAGE:e003f9bf246aced9_7_44]] , [[IMAGE:e003f9bf246aced9_7_45]] ). What is the investor’s coefficient of risk aversion ( [[IMAGE:e003f9bf246aced9_8_46]] )? (Note: [[IMAGE:e003f9bf246aced9_8_47]] represents the expected rate of return and [[IMAGE:e003f9bf246aced9_8_48]] represents the variance of the rate of return.)

A venture capitalist has a utility function of the form [[IMAGE:e003f9bf246aced9_8_49]] . She invests in a new firm with a 50% chance of failing. If the new firm succeeds, she expects to earn 256 million units. In the case of failure, she only gets 16 million units back. The venture capitalist has an option to purchase an insurance policy that pays her 240 million units if her investment fails. If she pays a price p for this policy, she would be sure to get [[IMAGE:e003f9bf246aced9_8_50]] million units regardless of success or failure. What would be the largest price ( [[IMAGE:e003f9bf246aced9_8_51]] ) that the venture capitalist would be willing to pay for such an insurance?

A pharmaceutical company start a new project to discover a drug. The project costs 500 thousand units, which is financed with a 400 thousand-unit loan and the remaining amount in equity. There is a 70% chance of a successful discovery, and in this case, the project generates a payoff of 900 thousand units in the next year. In the event of failure (30% chance), only 100 thousand units are recovered. The appropriate cost of capital is 10% per year. Based on the above data, answer the given subquestions.

What would be the appropriate promised rate of return that the creditor of the loan would demand?

A pharmaceutical company start a new project to discover a drug. The project costs 500 thousand units, which is financed with a 400 thousand-unit loan and the remaining amount in equity. There is a 70% chance of a successful discovery, and in this case, the project generates a payoff of 900 thousand units in the next year. In the event of failure (30% chance), only 100 thousand units are recovered. The appropriate cost of capital is 10% per year. Based on the above data, answer the given subquestions.

What is the expected payoff for the equity owner in the next year?

Suppose there are two assets, Asset 1 and Asset 2, with the following characteristics: • Expected Rate of Return: [[IMAGE:e003f9bf246aced9_9_52]] , [[IMAGE:e003f9bf246aced9_9_53]] • Standard Deviation: [[IMAGE:e003f9bf246aced9_9_54]] , [[IMAGE:e003f9bf246aced9_9_55]] • Correlation: [[IMAGE:e003f9bf246aced9_9_56]] Based on the above data, answer the given subquestions.

What would be the standard deviation of the rate of return of the equally weighted portfolio?

Suppose there are two assets, Asset 1 and Asset 2, with the following characteristics: • Expected Rate of Return: [[IMAGE:e003f9bf246aced9_9_52]] , [[IMAGE:e003f9bf246aced9_9_53]] • Standard Deviation: [[IMAGE:e003f9bf246aced9_9_54]] , [[IMAGE:e003f9bf246aced9_9_55]] • Correlation: [[IMAGE:e003f9bf246aced9_9_56]] Based on the above data, answer the given subquestions.

Suppose you would like to construct a portfolio with an expected rate of return of 19%. What weights would you put on Asset 1 and Asset 2, respectively?

Suppose there are two assets, Asset 1 and Asset 2, with the following characteristics: • Expected Rate of Return: [[IMAGE:e003f9bf246aced9_9_52]] , [[IMAGE:e003f9bf246aced9_9_53]] • Standard Deviation: [[IMAGE:e003f9bf246aced9_9_54]] , [[IMAGE:e003f9bf246aced9_9_55]] • Correlation: [[IMAGE:e003f9bf246aced9_9_56]] Based on the above data, answer the given subquestions.

What are the weights of Asset 1 and Asset 2 in the minimum variance portfolio?