An index comprises of three stocks, X,Y,Z, whose annual revenues are in the ratio of 1:2:3, respectively. What would be the percentage change in the factor weighted index between two points of time, if the prices of these three stocks move from 200,400,800 to 400,600,900, respectively?

A portfolio manager would like to retain atleast 10% of the investible funds in the form of cash. Competitive pressures force him to target portfolio return of 18%. He is confident of generating a return of 19% on the portfolio, and the cash would generate a maximum of 3% return. With Rs.100 crores of investible funds for management, how much is the liquidity policy dragging down the overall portfolio return from the target portfolio return in rupee terms.

An investor deposits Rs.200 lakhs today with a fund manager for a period of 5 years and gives a mandate that at any cost there should not be any erosion of this initial wealth by the end of 5 years. If the current risk free rate of return is 8%, what amounts can be invested by the fund manager in the risk free and risky assets, if the organisation, limits the leverage multiplier to a maximum of 2?

A company is expected to generate EBIT of Rs.200 crores next year. The estimated depreciation expense next year is Rs.50 crores. The company has a planned CAPEX of Rs.100 crores requiring Rs.50 crores towards additional working capital. As a policy the company always finances both CAPEX and working capital with a mix of debt and equity in the ratio of 1:1. The company plans to repay Rs.30 crores of its debt next year, pay Rs. 20 crores as interest, and it is in the marginal tax bracket of 30%. What is the estimate FCFE?

The expected FCFE of a firm for the next year is Rs.71 crores. The current market price of this firm's equity share is hovering around Rs.550. The consensus estimate of growth in cashflows into the foreseeable future is 5%. Analysts who follow the company regularly are of the opinion that this company's market beta would be 1.2. The 10 year Govt Bond Yield is 6% and the Indian markets are expected to generate a market risk premium of 8%. (NOTE: All calculations have to be rounded off to 2 decimal places). What is your opinion about the market valuation of this firm's equity share if you adopt the discounted cashflow model and no other perspective of your own?

A bond with a face value of Rs.1000 is currently sold at Rs.950. The coupon of this bond is 12%, which is paid once in an year, and the balance term to maturity of this bond is 10 years. If it has a callable feature and its first call can be invoked at the end of 7 years at a premium of 5% on the face value, then what is the Yield to Call of this bond?

A bond with a face value of Rs.1000 is currently sold at Rs.975. The coupon of this bond is 8%, which is paid twice a year. If the bond is going to be redeemed at a premium of 5% on the face value, then what is the Yield to Maturity of this bond?

A bond with a face value of Rs.1000 is currently sold at Rs.950. The coupon of this bond is 12%, which is paid once a year. If the bond is going to be redeemed at a premium of 5% on the face value, then what is the Duration of this bond?

A portfolio manager receives a mandate to manage funds of a trust requiring 14% return per annum. Keeping in view the risk appetite of the trust, the portfolio manager identifies two bonds A and B for investment. They are currently priced at Rs.880 and Rs.1000 respectively. Both bonds have a face value of Rs.1000, have similar number of years to maturity of 10 years, and are going to be redeemed at 5% premium, but have differing coupon rates of 11%(A) and 15%(B) which are paid once in a year. Which of the bonds was overvalued when the portfolio manager purchased them?

An Educational Institution approaches a PMS provider for managing its Fund of 50 lakhs. The investment horizon is 10 years. The portfolio manager setsup a portfolio of two bonds with a duration of 10 years on 1st January. Bond A with a Face Value of Rs.1000, paying 8% coupon once per year and maturing in 25 years, and another Bond B with a Face Value of Rs.1000, paying 5% coupon once a year and maturing in 30 years were selling on this day for Rs.750 and Rs.690. If the future 30 years would have a flat yield curve, how many A and B Bonds would be purchased by the bond manager?

An investor stipulates a hurdle rate of 20% p.a. on a Rs.1 crore fund assigned to a portfolio manager with all the discretion given to the PMS. As performance fee, the PMS decided to charge 30% over the hurdle rate, over and above a fixed charge of 1.5% p.a., Brokerage and other expenses of 0.2% and 0.5%, respectively, of the net AUM invested at the beginning of the year. During the first year, the portfolio earnt 35% on the initial fund invested. How much performance fee will be payable to the portfolio manager?

A fund manager is interested to calculate her performance fees for the second year of fund management. She started with a net fund value of Rs.1,28,96,000 and generated a return of 25% for the second year. As per the SEBI guidelines the high water mark fund value has to be Rs.1,32,80,000. The hurdle rate given by the client is 20% and the fund manager negotiated 30% towards performance fees. The fixed charges, brokerage and other expenses are 1.5%, 0.5% ad 0.2% respectively. How much performance fees can she charge this year?

Boom, Normal, and Recession are expected to occur with the probabilities of 55%, 35%, and 10%, in the coming year. In Boom, securities A and B can generate an annual return of 25%, 23%. In Normal, 19%, 17%, and in Recession, 13% and 11% respectively. What should be the proportions in which a fund manager need to invest in A and B to genrate an expected return of 20% from the portfolio?

A fund manager invested 15% and 85% of the fund in stocks A and B respectively. They generate an ex-ante returns of 21.7% and 19.7% for the coming year. The correlation coefficient of returns of the securities is 0.4 and their standard deviations are 4.01% each. What is the risk of the portfolio?

A fund manager invested 15% and 85% of the fund in stocks A and B respectively. They generate an ex-ante returns of 21.7% and 19.7% for the coming year. The risk of the portfolio is 25% . What is the utility of this portfolio to the inestor, and would she pick it up if her risk aversion index is 5 and the risk free rate of return is 6%?

A fund manager invested 15% and 85% of the fund in stocks A and B respectively. Their market beta is 1.2 and 1.5 respectively. If the expected risk free rate of return is 6% and the relevant market risk premium is 10%. Then what can be the expected rate of return of this portfolio, if the markets are efficient?

When the expected annual return on a portfolio is 18% and it variates with a standard deviation of 20%. Then what is the VaR of this portfolio, at 5% significance level, for a 10 days holding period? Assume a 250 days in a year and 1.96 as the relevant Z value for the calculation of VaR.

A PMS manager predicts prices of 30 stocks in a quarter of a normal year, each one coming from a different industry. During the previous one year he was successful in predicting 25,30,28,20 stocks respectively in the four predicting periods. How good is the manager in predicting? What metric would you like to use for the same? (round off to two decimals)

A PMS manager predicts prices of 20 stocks in a quarter of a normal year, each one coming from a different industry. During the previous one year he was successful in predicting 15,20,18,10 stocks respectively in the four predicting periods. What is the breadth of this manager and how much would be her Information Ratio? (round off to two decimals)

A Portfolio Manager is interested to protect the value of Rs.200 million of a portfolio. Currently options are available for the same maturity for a premium of Rs.5 Mn. What kind of option hedge would protect the desired value? In case on the date of maturity the value of portfolio drops by 10%, then what is the effective gain due to hedging with an option?

A portfolio generates 25% return during a particular year, with a volatility of 18%. In the same year the benchmark index generated 22% with a volatility of 15%. Incase the risk free rate of return during the same time is 8%. By how many basis points did the portfolio beat the benchmark? How do you measure the risk adjusted performance between the two, and how much is it?

If a portfolio and the index display a volatility of 18% and 15% respectively for generating returns of 25% and 22% respectively. Do you think that the portfolio actually has beat the market adjusting its risk to that of the market? Assume a risk free rate of return to be 8%.

A PMS manager receives Rs. 50 lakhs from a mutual benefit society to be invested in a portfolio of equity shares. Leaving Rs.5 lakhs in cash to encash opportune moments in the markets, the manager invests the rest in equal proportions in three equity shares K, L and M, each of which was bought at Rs.500, Rs.1000, and Rs.750 respectively. The manager would like to maintain the constant proportions strategy while rebalancing the portfolio at regular intervals. What action should the manager take when the prices of the three equity shares change to Rs.600, Rs.900, Rs.1200, (K, L, and M respectively), after 1 year ?

A PMS manager receives Rs. 50 lakhs from a mutual benefit society to be invested in a portfolio of equity shares. Leaving Rs.5 lakhs in cash to encash opportune moments in the markets, the manager invests the rest in equal proportions in three equity shares K, L and M, each of which was bought at Rs.500, Rs.1000, and Rs.750 respectively. The manager would like to maintain the constant proportions strategy while rebalancing the portfolio at regular intervals. What is the action prescribed w.r.t. equity share L. Roundup the number of equity shares?

An investor approaches a PMS provider with a 5 year plan of investment. She starts with Rs.50 lakhs at the beginning of the first year. Later at the beginning of each year from the 2nd to 4th years, she invests Rs.45 lakhs, Rs.35 lakhs, Rs. 60 lakhs, and Rs. 50 lakhs. The fund created by the manager generates net annual returns of 15%, 12%, -10%, -8%, 25%, for all the 5 years, after all the charges. What is the time weighted rate of return to the investot ignoring taxes?

An investor approaches a PMS provider with a 5 year plan of investment. She starts with Rs.50 lakhs at the beginning of the first year. Later at the beginning of each year from the 2nd to 4th years, she invests Rs.45 lakhs, Rs.35 lakhs, Rs. 60 lakhs, and Rs. 50 lakhs. The fund created by the manager generates net annual returns of 15%, 12%, -10%, -8%, 25%, for all the 5 years, after all the charges. What is the money weighted rate of return to the investot ignoring taxes?

An investor approaches a PMS provider with a 5 year plan of investment. She starts with Rs.50 lakhs at the beginning of the first year. Later at the beginning of each year from the 2nd to 4th years, she invests Rs.45 lakhs, Rs.35 lakhs, Rs. 60 lakhs, and Rs. 50 lakhs. The fund created by the manager generates net annual returns of 15%, 12%, -10%, -8%, 25%, for all the 5 years, after all the charges. What is simple arithmetic average rate of return for the investment horizon?

A fund manager chooses an investment for an investor which has shown a historical correlation of 0.8 with the benchmark index. If the volatility of this investment is 20%, and that of the benchmark index is 18%, the investor's tax bracket is 25%, the relevant risk free rate is 6%, and the historical market risk premium is 10%, then how much return should the manager generate on this investment (net of all charges and fees) before tax for the investor? Roundup the return to two decimals.

An investor aged 40 years approaches a PMS manager with a request to manage his surplus wealth, which is left out after completely diversifying and investing in all other traditional and required investments. This fund can be invested in a 100% equity portfolio. The fund manager creates such a portfolio which generates 25% return in the first year, when the relevant benchmark generated only 20%. However, the volatilities of both these portfolios were 22% and 15%. If the investor's portfolio displayed a correlation of 0.75 with that of the benchmark portfolio, and the relevant risk free rate was 6% for the 1 year period, which is the appropriate metric the fund manager should use to show his performance? (Choose between Sharpe's and Treynor's only)

A portfolio manager is about to report the gross and net returns to the investor on a 50 lakhs investment made a year ago. The investor set a target return of 15% and the portfolio manager negotiated a 20% management fee, over and above a fixed annual fee of 1.5% over the average value of asset under management. The other charges are 0.5% of the gross value of investment. What are the gross and net returns to be reported if the fund generated 20% during this year, with an exit load of 2%.