Stochastic Calculus Solution Manual

Problem 1.9. A stock when it is first issued provides funds for a company. Is the same true of an exchangetraded stock option? Discuss. An exchange-traded stock option provides no funds for the company. It is a

investor should invest $369.35 in asset A and the remaining $630.65 in asset B. The

2. St. Luke’s Convalescent Center has $200,000 in surplus funds that it wishes to invest in marketable securities. If transaction costs to buy and sell the securities are $2,200 and the securities will be

A firm’s intrinsic value refers to the true worth of stock in that firm which is calculated on return data and accurate risks. On the other hand, a firm’s current stock price talks about its market price as a whole as perceived by an

V= 1/2 ∑_(q=1)^Q▒〖(t_q- a_q^M )^τ (t_q- a_q^M )= 1/2 ∑_(q=1)^Q▒〖 e_q^τ e_q 〗 〗 Equation 3.5

13 Solution of task D2...................................................................................... 14 Reference...................................................................................................15

I΄(t) + (a+bt) I(t) = –[ α + β I(t) + γt]with I(t1)=0,0 ≤ t ≤ t1

Assume that a trial balance is prepared with an account balance of $8,900 listed as $9800 and an account balance of $1,000 listed as $100 . Identify the transposition and the

1. Write out the initial transaction and cash flows for the trade based on entering

The intrinsic value of Facebook stock was very difficult to find, since the company is relatively new and has been growing at an extreme rate. Based on the most recent sale of Facebook stock via a private transaction the per share price was $44 in March. However, based on the DCF analysis by professor Aswath Damodaran the intrinsic value of a single Facebook share would be $32.44. The problem is whenever using DCF analysis; the analysis is very sensitive to all assumptions uses, which were plenty in the case of Facebook. The price talk from underwriters varied immensely within the time from of February when the Red Herring was filed, all the way to May. At the very beginning, price talks were anywhere from $20 – mid $30’s. They were set to offer 337,415,352 shares. As the broader market continued in bullish trend and momentum for the Facebook IPO became greater. Price talks now shifted to $28-$35 range. Knowing that demand for the stock was said to be growing it was noted that many IPO are priced conservative to leave room for a pop on the first day of trading. On May 11 CNBC made a statement along the lines that demand was much greater than supply for the stock. Shortly after on May 14, the price talks had now moved to $34-$38 range and now offering 421,233,615 shares, the additional shares were all of insiders. This would set the companies valuation at

b. Plot the CAL along with a couple of indifference curves for the investor type identified above. c. Use Excel’s solver to maximize the investor’s utility and confirm that you get a 50% allocation in stocks. 3. You can invest in a risky asset with an expected rate of return of 20% per year and a standard deviation of 40% per year or a risk free asset earning 4% per year or a combination of the two. The borrowing rate is 9% per year. a. What is the range of risk aversion for which a client will neither borrow nor lend, that is, for which the allocation to this risky investment is 100%? b. Draw the Capital Allocation Line. Indicate the points corresponding to (i) 50% in the risk-less asset and 50% in the risky asset; and (ii) -50% in the riskless asset and 150% in the risky asset. c. Compute the expected rate of return and standard deviation for (i) and (ii). d. Suppose you have a target risk level of 50% per year. How would you construct a portfolio of the risky and the riskless asset to attain this target level of risk? What is the

Franco Modigliani and Merton Miller examined how a corporation should select securities to sell in order to attain an optimal mix between debt and equity, the mirror image of what Markowitz and Tobin had studied. Their findings led them to the conclusion that the market value of a firm is independent of its capital structure. In an efficient market, the market will place the same value on firms with equal earnings power and equal risk. Their most innovative contribution to the theory of finance was in elevating arbitrage to the level of a driving force. This Law of One Price states, “two assets with identical attributes should sell for the same price… a profitable opportunity will arise to sell the asset where it is overpriced and to buy it back when it is underpriced. The arbitrager will then lock in a sure profit, otherwise known as a free lunch.” (171) In effect, arbitragers actually fix the imperfections in the market by bidding away the

Q2. Provide a full-page plot of the Capital Allocation Line for the case in Q1. Label the axes and locate cash, D. Equity, D. Bonds, and your optimal complete portfolio clearly on the plot. You may draw this plot by hand.

Just after the student decided what he wanted to invest; He invested a small amount of money to prevent a big loss. The first investment was made in a mutual fund; This kind of stock grows slow, this makes them easier to manage and safer. The student invested $2,000 in a company called ‘American Funds Euro Pacific Growth A (AEPGX)’. It is a company that helps small businesses to growth; according to the charts the student thought it was a good idea to start investing in this company, since it is a long term the price of the stock rises or decreases in a slow rate.

The eventual returns to either of these investments would be the same. Therefore, the price of L must be the same as the price of U minus the money borrowed D, which is the value of L 's debt.