161.
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Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of .5. The alternative riskless investment in T-bills pays 5%. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio?
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162.
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An investor is going to invest some amount of total investment in a risky portfolio which has the expected return of 17% and standard deviation of 27%. The remaining amount will be invested in the T-bills which has the expected return on 7%. Suppose the same client as in the previous problem prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio’s standard deviation will not exceed 20%.
a. What is the investment proportion, y?
b. What is the expected rate of return on the overall portfolio?
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163.
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The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 1.5 and a residual standard deviation of 30%. What would make for a larger increase in the stock’s variance: an increase of .15 in its beta or an increase of 3% (from 30% to 33%) in its residual standard deviation?
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164.
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A portfolio of nondividend-paying stocks earned a geometric mean return of 5% between January 1, 2005, and December 31, 2011. The arithmetic mean return for the same period was 6%. If the market value of the portfolio at the beginning of 2005 was $100,000, what was the market value of the portfolio at the end of 2011?
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165.
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Assume that of your $10,000 portfolio, you invest $9,000 in stock X and $1,000 in stock Y. What is the expected return on your portfolio?
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166.
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a. Suppose the real interest rate is 3% per year, and the expected inflation rate is 8%. What is the nominal interest rate?
b. Suppose the expected inflation rate rises to 10%, but the real rate is unchanged. What happens to the nominal interest rate?
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167.
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The New Fund had average daily assets of $2.2 billion in the past year. The fund sold $400 million and purchased $500 million worth of stock during the year. What was its turnover ratio?
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168.
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You expect a tax-free municipal bond portfolio to provide a rate of return of 4%. Management fees of the fund are .6%. What fraction of portfolio income is given up to fees?
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169.
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City Street Fund has a portfolio of $450 million and liabilities of $10 million. If there are 44 million shares outstanding, what is the net asset value?
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170.
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The Closed Fund is a closed-end investment company with a portfolio currently worth $200 million. It has liabilities of $3 million and 5 million shares outstanding. What is the NAV of the fund?
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171.
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Which security has a higher effective annual interest rate?
a. A three-month T-bill with face value of $100,000 currently selling at $97,645.
b. A coupon bond selling at par and paying a 10% coupon semiannually.
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172.
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Treasury bonds paying an 8% coupon rate with semiannual payments currently sell at par value. What coupon rate would they have to pay in order to sell at par if they paid their coupons annually?
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173.
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Consider a bond paying a coupon rate of 10% per year semiannually when the market interest rate is only 4% per half-year. The bond has three years until maturity. Find the bond’s price today and six months from now after the next coupon is paid.
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174.
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A bond currently sells for $1,050, which gives it a yield to maturity of 6%. Suppose that if the yield increases by 25 basis points, the price of the bond falls to $1,025. What is the duration of this bond?
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175.
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Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6%. What is the duration if the yield to maturity is 10%?
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176.
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ATech has fixed costs of $7 million and profits of $4 million. Its competitor, ZTech, is roughly the same size and this year earned the same profits, $4 million. But it operates with fixed costs of $5 million and lower variable costs.
a. Which firm has higher operating leverage?
b. Which firm will likely have higher profits if the economy strengthens?
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177.
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IBX’s stock dividend at the end of this year is expected to be $2.15, and it is expected to grow at 11.2% per year forever. If the required rate of return on IBX stock is 15.2% per year, what is its intrinsic value?
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178.
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Calculate the price of a firm with a plowback ratio of .60 if its ROE is 20%. Current earnings, E1, will be $5 per share, and k = 12.5%.
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179.
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What if ROE is 10%, which is less than the market capitalization rate? Compare the firm’s price in this instance to that of a firm with the same ROE and E1 but a plowback ratio of b = 0.
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180.
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BC stock has an expected ROE of 12% per year, expected earnings per share of $2, and expected dividends of $1.50 per share. Its market capitalization rate is 10% per year. What is its expected growth rate, its price, and its P/E ratio?
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