Dr. P.V. Viswanath



Economics/Finance on the Web
Student Interest

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  1. If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
  2. If you cheat in any way, I reserve the right to give you no points for the exam, and to give you a failing grade for the course.
  3. You may bring in sheets with formulas, but no worked-out examples.
  4. You must explain all your answers.
  5. You have 2 hours to complete the exam.
  6. Do question 1 and any three of the remaining questions. Make sure to provide as much information as possible, so I can give you partial credit, if necessary.

1. Read the article below and answer the following questions:

  1. (10 points) Ambac plans to cut its dividend "in its first steps towards bolstering its credit ratings." Why should cutting dividends affect Ambac's credit ratings?
  2. Shares of Assured rose $2.87, or 13%, to $25.65 on the NYSE, following investor Wilbur Ross investment of as much as $1 billion in Assured.
    1. (7 points) Why did Assured's share prices rise?
    2. (8 points) What, do you think, happened to Assured's bond prices? Why?

Ambac to Cut Dividend, Freeze Some Business
By KAREN RICHARDSON, WSJ March 1, 2008; Page B5

In its first steps toward bolstering its credit ratings, bond insurer Ambac Financial Group Inc. will cut its dividend and stop writing policies for complex debt securities for the next six months.

The moves, which are similar to measures recently announced by rival MBIA Inc., are part of Ambac's strategy to preserve its top-notch triple-A rating, which it needs to compete in the market of insuring municipal bonds. Ambac said the plans were partly in response to comments by Moody's Investors Service, which continues to review the bond insurer for possible downgrade.

"Once our triple-A ratings are fully confirmed by Standard & Poor's and Moody's, we will be in a position to take advantage of the current market environment," Ambac Chief Executive Michael Callen said. Ambac will cease underwriting policies using credit-default swaps and will stop writing investment agreements. It also will discontinue writing business in some international structured-finance sectors, he said. He said these moves would help free up about $600 million in capital.

Moody's said Ambac still may lose its triple-A rating but suggested that a plan Ambac is working on to raise new capital could be enough to avoid a downgrade. Ambac is trying to raise at least $2 billion, said people familiar with the matter. The bond insurer falls $2 billion short of Moody's "target" level requirement for a stable triple-A rating. In New York Stock Exchange trading Friday, Ambac shares fell 66 cents, or 5.6%, to $11.14.

Also, Ambac on Friday said it received a subpoena from Massachusetts that seeks information concerning Massachusetts public issuer bonds. It also said it has been named in at least four federal lawsuits seeking class-action status, alleging false and misleading statements regarding its insurance coverage on collateralized debt obligation contracts and conducting alleged insider trading.

Ambac and MBIA, the two biggest participants in the $2.3 trillion business of guaranteeing the interest and principal on bonds in the event of default, face new competition from a unit formed by billionaire Warren Buffett's Berkshire Hathaway Inc. Berkshire Hathaway Assurance Corp., an insurer he launched in December to guarantee municipal bonds, is swiftly building market share.

In recent days, ratings firms have bestowed triple-A ratings on municipal bonds insured by the Berkshire venture, months before competitors and some analysts predicted. On Friday, Maryland's insurance department granted Berkshire a license to do business in that state. The company already has guaranteed more than 100 municipal-bond offerings.

Meanwhile, MBIA said it expects to make loss payments, before reinsurance, of $700 million to $800 million for 2008. The loss payments would be mainly related to insured credits in the residential-mortgage-backed securities and home-equity sectors. MBIA's shares fell $1.09, or 7.8%, to $12.97, also on the Big Board.

Shares of bond insurer Assured Guaranty Ltd. rose Friday after disclosing that investor Wilbur Ross will provide as much as $1 billion to strengthen its business. Mr. Ross will get a seat on Assured Guaranty's board. Shares of Assured rose $2.87, or 13%, to $25.65 on the NYSE.

Assured is seen as having the fewest problems among several bond insurers, and the deal with Mr. Ross is likely to put more pressure on Ambac and MBIA.

2. (25 points) You are interested in buying a house. Under normal circumstances, you probably would have financed the purchase using an adjustable-rate mortgage, because you fancy yourself able to forecast interest rates, and you'd be able to switch to a fixed-rate mortgage if the outlook for interest rates looked bad (or so you think, anyway). However, given the current credit crunch and uncertainty, your spouse tries to convince you to go for a fixed-rate mortgage. All you will agree to is to consider both alternatives. The house itself costs $430,000, but you have $130,000 of your own money, which you can put up as a down-payment. (This is particularly lucky because in the current situation, bankers are requesting a bigger down payment -- see "Some Borrowers Hit New Snag In Refinancing, WSJ, March 6 2008, section D1 and you might not have got the loan if you hadn't had enough of a down payment.)

The banker offers you two alternatives -- a 15-year fixed rate loan at 7.5% APR with monthly payments, the first payment to be made immediately. The second alternative is an adjustable rate loan starting out at a stated rate of 5% and adjustable once in three years. You believe that in three years time, you can convert the rate to a fixed rate of 8.5%.

  1. What is the sequence of payments you expect to make on the adjustable-rate loan?
  2. Considering the greater uncertainty in the second alternative, you believe that the right discount rate for the second loan is closer to 8%, while you think the fixed rate loan is fairly priced. That is, you are not inclined to use the adjustable rate option if the yield-to-maturity on the loan is any more than 8%. Using this assumption, what is the present value of the adjustable rate loan? Which is the better deal for you? (Hint: If the present value of the adjustable rate loan is less than $300,000, it's a good deal; the fixed rate loan is fairly priced and, hence, has an NPV of zero.)

3. (25 points) Suppose you estimate the current bond-equivalent yields for 6-month money, 1 year money, 18-month money and 2 year money as 2.07%, 2.1%, 2.11% and 2.14% (that is the bond-equivalent yields of zero-coupon Treasury bills; remember a bond-equivalent annual yield is twice the six-month yield). What is the price of a 2 year, 2 percent T-note with a face value of $1000?

(For your information, such a note was auctioned by the Treasury on Feb. 27, 2008. It was issued on Feb. 29, 2008 and will mature on Feb. 28, 2010. The lowest price was 99.912254 per $100 of face value, corresponding to a yield of 2.045%. Five percent of the competitive bids that were accepted quoted less than 1.97%. For more information, see http://www.publicdebt.treas.gov/of/releases/2008/ofk0227081.pdf).

4. (25 points) In an article in the WSJ of March 4th 2008 (Bank Dividends Lack a Case in Tough Times, page C1), we read: "Citigroup cut its common-stock dividend by 40% in January. Yet, it's still committed to paying $1.28 a share a year." Its last dividend of 32 cents was paid on January 31, 2008. (For convenience, assume that today's date is February 1, 2008.) For the four quarters prior to that, it paid 54 cents a share, and for the four quarters before even that, the dividend was 49 cents a share. Clearly, Citigroup has been paying a hefty dividend (even now, its dividend yield -- that is, the dividend per share divided by price per share -- is 5.78%) and has regularly increased dividends. You believe, therefore, that Citigroup will raise dividends back to 54 cents after four more quarters of 32 cent per share dividends (that is, a 54 cent dividend will paid, once more, on April 30, 2009. Thereafter, you believe dividends will grow at the rate of 1% per quarter forever (even though it is customary to keep quarterly dividends the same for a whole year). The capitalization (or discount) rate that's appropriate to Citigroup is, you believe 3.5% per quarter.

  1. Assuming that today's date is , what should be the price at which Citigroup stock trades?
  2. According to Yahoo, the closing price of Citibank on March 6, 2008 was $21.17. Is Citibank, then, overpriced or underpriced, given your answer in part. (a). How would you reconcile the discrepancy between the actual price and your estimated price?

5. (25 points) Answer any four of the following questions:

  1. What does the Efficient Markets Hypothesis say?
  2. Suppose two stocks have the same current earnings. One stock however, has a higher forecasted earnings growth rate than the other. Which of the two stocks will have a higher price, the one with the higher earnings growth rate or the one with the lower growth rate? (Assume that the required rate of return is the same for both stocks.)
  3. You are on the board of a company. The cost of equity for this company is 14% per annum. The question before the Board is whether the company should cut dividends and invest in a project that will yield 14% per annum, as well. The proposal's proponent argues that this will increase the growth rate of earnings, citing the well-known formula that Growth Rate = (Return on Equity)x(1-Payout Ratio). Do you think he is correct? Why or why not? (Hint: Do not be misled by the fact that the proponent is male; even males get it right sometimes; but they can also get it wrong!)
  4. Corporate bond yields are expected to go down over the course of the next year, even they are high, right now. What will happen to bond prices?
  5. A bond with a face value of $1000 is selling at a price of $1020. The yield to maturity on the bond is 8%. You'd like to know the coupon rate on the bond. Your good friend, Daiyu, says that it's impossible to say anything at all about the coupon rate without knowing the maturity of the bond. Is she right?

Midterm Solutions

1. a. Cutting dividends should increase the amount of assets available as security for bond holders. This will make the bonds, themselves, less risky and will increase the probability of their repayment. Hence bond ratings shoudl improve and so should bond prices.

b. Assured's share prices probably rose for several reasons. One, it would now have more capital, thus enabling it to weather the credit crunch; creditors would have more confidence in Assured and would be more willing to continue to do business with Assured. Second, Wilbur Ross's willingness to invest in Assured is a positive signal; investors will probably assume that Wilbur Ross had positive information about the firm that they don't have access to.

2.a. For the first three years, you would make payments according to the beginning rate, i.e. 5%. Since this is an APR, the monthly rate is .05/12 or 0.0041667. The amount borrowed is 430,000-130,000 or $300,000. We use the PV of an annuity formula to compute the monthly payment. Since payments are made at the beginning of the month, the formula can be written as: PV = C + (C/r)[1-(1+r)-n-1]. Using the quantities that apply to our example, we have 300,000 = C + (C/0.0041667)[1-(1.0041667)-179]. Solving, we find C = 2362.537. So under the adjustable rate mortgage, you would pay $2362.537 per month for the first 36 months (again, payments would be made at the beginning of the month). At the end of the 36 months, the present value of the payments yet to be made (i.e. the amount that you would have to pay to the bank, if you wanted to pay the loan off in full) would be computed using the same formula, i.e. 2362.537 + (2362.537/0.0041667)[1-(1.0041667)-143] = $256,504.

At this point, you believe, the rate would jump to 8.5 and stay there for the remainder of the loan (since you would convert it to a fixed rate loan at that time). The monthly rate, therefore, would be 0.085/12 = 0.0070833. We would then compute the monthly payment at this point by solving the following formula: 256,504 = C + (C/0.0070833)[1-(1.0070833)-143]. Solving, we get 2827.31.

Hence there would be 36 payments of 2362.537, followed by 144 payments of 2827.31, all payments being at the beginning of the month.

b. To compute the present value of these payments, we need to discount these payments at the rate of 8%, i.e. 0.006667 per month.

The present value (in three years) of the second set of 144 payments is 2827.31 + (2827.31/0.006667)[1-(1.006667)-143] = 262,936.11. The present value today of this amount is 262,936.11/(1.006667)36 = 206,997.67.

The present value today of the first set of 36 payments is 2362.537 + (2362.537/0.006667)[1-(1.006667)-35] = 75,895.44. Adding this to the present value of the second set of payments, we get $282,893.11, which is less than $300,000. Hence you would go with the adjustable rate mortgage.

3. The cashflows are simply equal to the coupon for the first three payments; for the last payment, it consists of the coupon plus the face value. (The coupon itself is half of the coupon rate times the face value, every six months.) The discount rates are as given below, but they have to be divided by two to get the six-monthly rate. For example, the six-monthly discount rate for 1 year is 2.1/2 = 1.05%. Hence the present value of those $10 is 10/(1.015)2 = 9.69. The other numbers are computed in the same way. Adding up, we get the bond price to be $997.2849.

Period Cashflow PV bond-equiv
0.5 10 9.89756 2.07
1 10 9.793262 2.1
1.5 10 9.690063 2.11
2 1010 967.9041 2.14

4. The firm is expected to pay 32 cents for the next four quarters, following which, it will resume paying dividends at the rate of 54 cents/quarter. That is, its next payment of the 32 cents dividend is on April 30, 2008; its first payment of 54 cents will be on April 1, 2009.

  1. Its terminal Value on Feb. 1, 2009 can be computed by using the Dividend Discount Model with the constant growth parameter: Price = 0.54/(.035-0.01) = 21.6. Present value of this stream is 21.6/(1.035)4 = 18.82. Present Value of an annuity of 32 cents for four quarters is (0.32/.035)/[1-(1.035)-4] = 1.18. Summing, we get $20.
  2. At a price of $21.17, the stock would seem to be overpriced. Even if we adjust the price so that it is computed as of March 6, we would still only get a price of 20(1.035)1/3 = $20.23. Of course, the $21.17 price is one month later than the date that the $20 price was computed; hence new information could have come in. Alternatively, the $20 price could be based on an incorrect (ex-ante) forecast.


  1. The Efficient Markets Hypothesis says that an asset's current price fully reflects all publicly available information about future economic fundamentals affecting the asset's value.
  2. The stock with the higher forecasted earnings growth will have a higher price, since ceteris paribus it should have higher dividends.
  3. If the cost of equity is 14% and the rate of return on the project for equityholders is also 14%, then the NPV of the project for equityholders is zero. Hence this will not affect the stock price even though the growth rate of earnings will undoubtedly go up (albeit from a lower level, since current dividends will have to be cut).
  4. If yields go down, bond prices will go up, since the present value of future coupons (and principal repayment) will be higher.
  5. You cannot compute the yield to maturity exactly. However, since the bond is selling at a premium, we know that the coupon rate must be higher than the yield to maturity, i.e. the coupon rate must be greater than 8% and this is independent of the maturity of the bond.



  1. If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
  2. If you cheat in any way, I reserve the right to give you no points for the exam, and to give you a failing grade for the course.
  3. You may bring in sheets with formulas, but no worked-out examples.
  4. You must explain all your answers.
  5. You have 2 hours to complete the exam; please make sure to attempt all the questions, so I can give you partial credit, if necessary.

1. Read the article below and answer these questions:

  1. (6 points) Which industry stocks have a higher beta, coal or steel? (You can figure this out by looking at the figure below).
  2. (6 points) What statement in the article would lead you to conclude that steel stocks have a beta much greater than one?
  3. (9 points) ETFs or Exchange-Traded Funds (http://finance.yahoo.com/etf/education/01) are like mutual funds. There are at least two kinds of ETFs: one is Market Vectors Agribusiness ETF (NYSE:MOO), which is composed of 40 companies that are primarily involved in the agricultural business; another is PowerShares DB Agriculture ETF (NYSE:DBA), which invests in futures contracts in soy beans, corn, wheat, and sugar, with 25% being associated towards each commodity. Why does the article say that agricultural ETFs provide diversification? In what sense do such ETFs not provide diversification?

Global Growth Creates Market Winners

Stocks are down so far this year, the U.S. economy could be in the midst of a recession, and the housing market's troubles could linger for many months.

But a handful of stocks and sectors are soaring in 2008, believe it or not. Some of them, such as some companies in the steel and agricultural businesses, could continue to generate strong gains, analysts say, though others, such as some coal and energy companies, look like riskier prospects.

Last week saw big gains in the stock market, with the Dow Jones Industrial Average surging 4.3% and the Nasdaq Composite Index advancing 4.9%. One boost came from earnings announcements by financial giants Citigroup and Merrill Lynch that were dismal, but not as bad as some investors had feared. Meanwhile, technology companies Google and Intel reported strong earnings.

So far this year, the Dow is down 3.1% and the Nasdaq is down 9.4%.

Despite last week's advance, analysts worry that stocks could feel more pressure as earnings season continues. "We expect generally disappointing results and a swath of lowered profit guidance that will drive the [market] lower in coming weeks," says David Kostin, a strategist at Goldman Sachs.

Strong as Steel

But companies that benefit from global growth continue to generate healthy gains. One such thriving industry is the steel business. The 20% advance so far this year in the Dow Jones Wilshire U.S. Steel Index is surprising -- in the past, steel producers suffered when the U.S. economy slumped.

Today, however, U.S. consumption amounts to just 8% of global steel demand. Growth around the globe is proving so strong that less foreign steel is being imported into the U.S., because so much of it is being used abroad. And a weak dollar is making steel imports more expensive.

That's leaving a higher market share for U.S. steel producers, especially when it comes to higher-grade steel. So even though U.S. demand is more challenged, amid the economy's slowdown, the supply shrinkage is more than offsetting it, enabling steel prices to climb.

In fact, steel prices in the U.S. more than doubled in the last six months, and exports from China, Russia and Brazil are dropping.

"We've never seen anything like this," says Aldo Mazzaferro, an analyst at Goldman Sachs who's a fan of steel stocks. "It's gone from a tight market around the globe to a shortage, and it's very unlikely we'll have easing."

He's among the fans of U.S. Steel, which is up 28% this year and is expected to see earnings rise 19% over the next 12 months. The company has more debt than some others in the business, but not enough to elicit concern, analysts say.

Nucor, up 25% this year, is another steel stock with impressive prospects, some say. The company, which sports a strong balance sheet and well-respected management, is expected to grow earnings 30% in the next 12 months, but only trades at a price-earnings multiple of 11. In the past month, analysts raised estimates for the current quarter's earnings by 13%.

The cost of the scrap metal that Nucor buys has been relatively flat, even as the steel it produces rises in price, helping the company's profit margins.

What would hurt steel stocks? They're likely to suffer if the global economy goes into a recession or the dollar jumps, making imports cheaper. Mr. Mazzaferro says AK Steel Holding and Steel Dynamics are more expensive, and therefore are less attractive.

Bumper Crop

Meanwhile, demand is surging for agricultural commodities -- from grains and sugar to fertilizers and oilseeds (grains valued for their oil content). One reason: increased consumption of grain-fed beef as the middle class in emerging-market nations grows and their diets begin to look more like those of Western consumers.

Potash Corp. of Saskatchewan and Mosaic, two makers of fertilizer and animal-feed products, have seen their shares more than triple and more than quadruple, respectively, in the past year. They're up 42% and 43% so far in 2008.

But the run-up has some financial advisers suggesting that investors shift to exchange-traded funds that invest in agricultural commodities, such as Powershares DB Agricultural Fund, which is up more than 50% over the past year and up 18% so far in 2008.

ETFs are low-cost securities that trade throughout the day like stocks. Agricultural ETFs usually track a basket of commodities, providing more diversification and safety than an individual stock. Another option: the Opta Lehman Brothers Commodity Pure Beta Agricultural Total Return exchange-traded note.

Be Resourceful

Energy-related shares have been strong in the past year, especially shares of coal companies. Among the stock market's bright spots so far in 2008, a Dow Jones Wilshire index of U.S. oil-and-gas exploration and production stocks is up 16% while an index of coal stocks is up 21%.

But energy stockpiles are full -- and if global growth slips a bit, some energy companies could come under pressure. Exploration-and-production company Devon Energy, up 33% this year, could fall sharply if oil tumbles, some say, as could XTO Energy, up 32% in 2008.

Analysts at Friedman Billings Ramsey are bullish on a small coal provider, Patriot Coal. The stock already is up 57% this year, but the firm argues that a recent merger and growing production will help the company.

"Patriot could sign 2009 contracts at a price well above our revised assumptions," says Luther Lu, an FBR analyst, who notes that Patriot has a strong balance sheet.

2. You have the ability to invest in a corporate bond issued by Delta Airlines with an expected return of 5% per annum; you can also invest in Delta stock. You want to have some idea of the expected return if you do invest in Delta. Knowing that, according to the CAPM, the expected return on Delta is related to its beta, you check out Yahoo and Google for Delta's beta. Unfortunately, neither stock has any information on Delta's beta. Figuring out that airlines should be similar to each other, you check out some other airlines. According to Google, American Airlines has a beta of 4.46, while US Airways has a beta of 3.52. Southwest has a beta of 0.26. The 10-year Treasury note yielded 3.771 at close of trading on May 1. The standard deviation of returns on Delta stock, as estimated from the realized monthly returns on Delta stock between January 1990 to October 2005, is 46% per annum.

  1. (5 points) What does a stock's beta measure?
  2. (10 points) Why is Southwest's beta so different from that of American and US Airways. Keep in mind two things while answering -- one, the nature of beta (i.e. what beta represents) and two, that betas on Google are probably computed as the estimated slope of a regression of stock returns on S&P 500 returns (the S&P is considered a proxy for the market portfolio).
  3. (5 points) If you assume that Delta's beta is a simple average of the Google betas of American and US Airways, what would the required rate of return on Delta be (assuming a market risk premium of 8%)?
  4. (5 points) If you want to earn an expected return of 0.5% per week, which is equivalent to an annual return of 29.6%, what proportion of your portfolio would you invest in Delta stock and what proportion in the Delta bond?
  5. (5 points) What would be the standard deviation of returns on your portfolio determined in part d above, assuming a zero correlation between returns on the Delta stock and the Delta bond?
  6. (5 points) Is it reasonable to assume a zero correlation between the Delta stock and the Delta bond?

3. Disgusted by your inability to find a good measure of Delta's beta, you go to two other stocks, Potash Corp./Saskatchewan (USA) (NYSE:POT) and Devon Energy Corp. (NYSE: DVN). This time, instead of using the CAPM approach to forecasting expected future return, you decide to simply use historical data on the two stocks for the past year. Using weekly return data (from Google, though it's unclear if these returns are adjusted for dividends as they should be), you determine that the expected weekly return is 0.95% for DVN with a standard deviation of returns of 3.8%. The expected weekly return for POT is 2.6% with a standard deviation of returns of 6.4%. The correlation coefficient between the returns on these two stocks is 0.63.

  1. (10 points) If you can also invest in the 10-year T-note referred to above, which would yield a weekly return of (1.03771)1/52 = 0.07%, what are the portfolio proportions of the tangent portfolio (consisting of DVN and POT) that you would invest in?
  2. (5 points) If you want a return of 0.5% per week, how much would you invest in the T-note?
  3. (5 points) What would be the standard deviation of returns on the combined optimal portfolio (consisting of investments in the T-note and in the tangent portfolio)

4. Answer any three of the following questions(24 points):

  1. What are the determinants of the equilibrium expected rate of return on the market portfolio?
  2. What is the difference between risk and uncertainty? Give an example.
  3. What is the difference between hedging and insuring as means of risk transfer?
  4. What is the difference between moral hazard and adverse selection?

Final Exam Solution


  1. Steel stocks and coal stocks, both, move together with the broader market. However, it is clear from the figure that coal stocks have a greater amplitude than steel. Hence steel stocks have a greater beta than coal stocks.
  2. "The 20% advance so far this year in the Dow Jones Wilshire U.S. Steel Index is surprising -- in the past, steel producers suffered when the U.S. economy slumped." The second part of the sentence above suggests that market movements (at least downward ones) are magnified in the steel sector.
    The following statement also leads to a similar conclusion (though it would imply a global beta greater than one): "What would hurt steel stocks? They're likely to suffer if the global economy goes into a recession or the dollar jumps, making imports cheaper."
  3. "Agricultural ETFs usually track a basket of commodities, providing more diversification and safety than an individual stock." Since both kinds of agricultural ETFs track more than one commodity (or more than one agricultural stock), stock-specific or commodity-specific fluctuations are likely to cancel each other out. For example, if there's a shortage of rice abroad that would affect the price of rice, but it may not affect the price of corn. Similarly, labor unrest in one company would likely be uncorrelated with changes in the prices of the other agricultural stocks.
    However, the kind of diversification that any sector ETF can provide is going to be limited because all stocks in a given sector respond to sector-specific events. Thus, if corn is being used increasingly for the production of biofuels because of tax incentives, this will affect the price of all food crops to a greater or less extent. Similarly, if the US comes to an agreement with the EU to allow the EU to sell its food products in the US with a lower tariff rate, this will affect the entire agricultural sector.


  1. A stock's beta measures it non-diversifiable or market risk. It is a measure of the rate at which the variance of the market portfolio would change if the portfolio weight of the stock changed a small amount. It also measures the sensitivity of the return on the stock to changes in the return on the market portfolio.
  2. Southwest may have a low beta because it's a no-frills carrier. People treat flying on Southwest as a necessity -- they may not change their travel habits that much because of changes in their wealth. The legacy carriers, American and US Airways, on the other hand, are closer to full-service carriers. Their prices are higher, and their customers may cut back on air travel if times are bad, or they might switch to Southwest; if times are good, Southwest fliers may switch to US Airways and American Airlines.
  3. Delta's beta is a simple average of the Google betas of American and US Airways, its beta would be (4.46+3.52)/3.99. The required rate of return on Delta would be 3.711+3.99(7.5) = 33.636%
  4. If you wanted to earn an annual return of 29.6%, you would invest x% in Delta, where 33.636x + 5(1-x) = 29.6. Solving, we find x = 0.859.
  5. If the correlation coefficient between the returns on the Delta bond and Delta stock were zero, then the standard deviation of returns on the portfolio would be 0.859*46 = 39.514% per annum.
  6. No; since they would both be affected, more or less in the same fashion, by the same events, they would be positive correlated.


  1. The tangent portfolio is given by the formula , where the two risky assets are labelled D and E. If we use D to represent POT, we find that the proportion that POT would represent in the tangent portfolio is [(2.6 - 0.07)(3.8)2 - (0.95 - 0.07)(0.63)(6.4)(3.8)]/[(2.6 - 0.07)(3.8)2 + (0.95-0.07)(6.4)2 - (2.6 - 0.07 + 0.95 - 0.07)(0.63)(6.4)(3.8)] = 1.1337. Hence the proportion in DVN would be 1-1.1337 or -0.1337.
  2. The expected return on the tangency portfolio would be 2.6(1.1337) - (0.95)(0.1337) = 2.8206% per week. Hence, in order to obtain a return of 0.5% per week, you'd invest x% in the T-note, where 0.07x + 2.8206(1-x) = 0.5. Solving, we find x = 0.8437.
  3. The variance of returns on the tangency portfolio is (1.1337*6.4)2 + (0.1337*3.8)2 + 2(1.1337)(0.1337)(0.63)(6.4)(3.8) = 57.54778; hence the standard deviation of returns is (57.54778)0.5 = 7.586% per week. Hence the standard deviation of returns on the combined optimal portfolio would be 0.8437(7.586) = 6.4% per week.


  1. The determinants of the equilibrium expected rate of return on the market portfolio are: the expected productivity of the capital stock, the degree of uncertainty about the productivity of capital goods, household intertemporal preferences for consumption, and average risk aversion on the part of investors.
  2. Uncertainty exists when economic agents do not know for sure what will be the outcome of an economic quantity. Risk is when that uncertainty matters. Thus, in the context of asset pricing, uncertainty about next period's return on an asset might exist. However, as long as that uncertainty can be got rid of with very little additional cost by holding a diversified portfolio, it is not risk. Only non-diversifiable uncertainty is risk.
  3. Hedging is when uncertainty is eliminated by giving up the upside along with the downside. Obviously, this would require very little or no up-front payment, since the surrender of the upside compensates fully or partially for protection against the downside. Insurance is when the investor seeks protection only against downside movements in his/her wealth without giving up any upside. An up-front price will usually have to be paid for this.
  4. Adverse selection occurs because of information asymmetry before parties enter into a contract. Usually one party offers a contract, and the second party can accept or defer. Adverse selection is when the second party accepts, and has characteristics that would make the contract undesirable for the first party.
    Moral hazard occurs after the two parties have entered into a contract. If it is costly to observe the actions of one party, that party might take actions that would decrease the value of the contract to the other party. Since these actions are unobservable, the secodn party would not be able to incorporate the impact of these costly actions into the contract.