Problem 1

a. How is Dow Jones index computed? Write 1 paragraph on the history of when the Dow
Jones Index was first initiated. Computation Method: Dow Jones is a price-weighted index. So, to calculate the DJIA, the sum of the prices of all 30 stocks is divided by a devisor which is named the Dow Divisor. The divisor is adjusted in case of stock splits, spinoffs or similar structural changes, to ensure that such events do not in themselves alter the numerical value of the DJIA. Early on, the initial divisor was composed of the original number of component companies; which made the DJIA at first, a simple arithmetic average. The present divisor, after many adjustments, is less than one (meaning the index is larger than the sum of the prices of the components). That is:

Where p is the prices of the component stocks and d is the Dow Divisor.
Events like stock splits or changes in the list of the companies composing the index alter the sum of the component prices. In these cases, in order to avoid discontinuity in the index, the Dow Divisor is updated so that the quotations right before and after the event coincides:

History: Dow Jones & Co. was founded in 1882 by Charles Dow, Edward Jones and Charles Bergstresser. Despite popular belief, the first averages were not published in the Wall Street Journal but in its precursor, called the Customer's Afternoon Letter. The first averages didn't even include any industrial stocks. The focus was on the growth stocks of the time, mainly transportation companies. This means that the first Dow Jones Index included nine railroad stocks, a steamship line and a communications company. This average eventually evolved into the transportation Average. It wasn't until May 26, 1896, that Dow split transportation and industrials into two different averages, creating what we know now as the Dow Jones Industrial Average.
Charles Dow had the vision to create a benchmark that would project general market conditions and therefore help investors bewildered by fractional dollar changes. It was a revolutionary idea at the time, but its implementation was simple. The averages were, well, plain old averages. To calculate the first average, Dow added up the stock prices and divided by 11 - the number of stocks included in the index.
Today, the DJIA is a benchmark that tracks American stocks that are considered to be the leaders of the economy and are on the Nasdaq and NYSE. The DJIA covers 30 large-cap companies, which are subjectively picked by the editors of the Wall Street Journal. Over the years, companies in the index have been changed to ensure the index stays current in its measure of the U.S. economy. In fact, of the initial companies included in the average, only General Electric remains as part of the modern-day average.
The changes won’t cause any disruption in the level of the Index. The divisor is used to offset the changes. Events like replacement oraddition in the list of the companies composing the index alter the sum of the component prices. In these cases, in order to avoid discontinuity in the index, the Dow Divisor is updated so that the quotations right before and after the event coincides:

Current Devisor (February 13, 2015): 0.15571590501117

Visa Inc. had four-for-one stock split that did not affect the overall value of the Dow Jones Industrial Average, .But the credit card company’s weighting in the blue-chip index dropped significantly, meaning other companies took the driver’s seat in steering the Dow.
That’s because the Dow is price-weighted index. Dow stocks with the highest prices have the largest impact. Visa had a 9.1% weighting in the Dow before split. That’s the most of any Dow component by a long shot. Goldman Sachs Group Inc.GS -0.41% had the second-heaviest weighting (and price) at 6.5%. After Visa’s four-for-one split, the share price dropped from $248 to $62, pushing Visa’s weight to 2.5%. That put it in the lower third of companies in the Dow. As a result, Goldman’s impact rose to 7%.

b. General Electric stock call-option with a strike price of $25 and with expiration date of January 15,2016 and strike price of 15.00 $ gives the holder right to purchase 100 share of general electric at price of 25.00$ on or before the expiration date.

C. Generally, It is a future contracts calls for delivery 1000 barrel Crude oil at a specified price( currently 69.63$ ) per barrel in February 2020.Details of delivery are as below:

Delivery shall be made free-on-board ("F.O.B.") at any pipeline or storage facility in Cushing, Oklahoma with pipeline access to Enterprise, Cushing storage or Enbridge, Cushing storage. Delivery shall be made in accordance with all applicable Federal executive orders and all applicable Federal, state and local laws and regulations.

At buyer's option, delivery shall be made by any of the following methods: (1) by interfacility transfer ("pumpover") into a designated pipeline or storage facility with access to seller's incoming pipeline or storage facility; (2) by in-line (or in-system) transfer, or book-out of title to the buyer; or (3) if the seller agrees to such transfer and if the facility used by the seller allows for such transfer, without physical movement of product, by in-tank transfer of title to the buyer.

A) Delivery shall take place no earlier than the first calendar day of the delivery month and no later than the last calendar day of the delivery month.

B) It is the short's obligation to ensure that its crude oil receipts, including each specific foreign crude oil stream, if applicable, are available to begin flowing ratably in Cushing, Oklahoma by the first day of the delivery month, in accord with generally accepted pipeline scheduling practices.

B) Transfer of title-The seller shall give the buyer pipeline C) ticket, any other quantitative certificates and all appropriate documents upon receipt of payment.

The seller shall provide preliminary confirmation of title transfer at the time of delivery by telex or other appropriate form of documentation.
Following chart represents the historical price of oil future with maturity of five years from now (February 2019).

d)Yield Curve: A line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but differing maturity dates. The most frequently reported yield curve compares the three-month, two-year, five-year and 30-year U.S. Treasury debt. This yield curve is used as a benchmark for other debt in the market, such as mortgage rates or bank lending rates. The curve is also used to predict changes in economic output and growth.

Yield curve for Government bonds in U.S is as below:

The yield curves for Grade AAA, Grade AA and Grade and Grade A are as follow:

e. The S&P 500, or the Standard & Poor's 500, is an American stock market index based on the market capitalizations of 500 large companies having common stock listed on the NYSE or NASDAQ. The S&P 500 index components and their weightings are determined by S&P Dow Jones Indices .The index is computed by weighted average market capitalization.
The first step in this methodology is to compute the market capitalization of each component in the index. This is done by taking the number of outstanding shares of each company and multiplying that number by the company's current share price, or market value. Next, the market capitalizations for all 500 component stocks are summed to obtain the total market capitalization of the S&P 500.Then, to calculate the value of the S&P 500 Index, the sum of the adjusted market capitalization of all 500 stocks is divided by a factor, usually referred to as the Divisor. For. The Divisor is considered to be proprietary to the firm. However, the Divisor's value is approximately 8.9 billion.
The formula to calculate the S&P 500 Index value is:

Problem 2. a) It is assumed that initial margin percentage is 50 and rate on margin loan is 0 .current price of Google stock price is 541.5 assume that after 6 month the price of Google stock it will be 560.Then, the return of investment will be % 4.99 .If we do not buy on margin the return on investment will be % 2.49 which is half. However, if the price drop to 520 the return on investment will be -7.94 while if we do not buy on margin, the return of investment will be -3.97. Leverage is a double-edged sword, amplifying losses and gains to the same degree. In fact, one of the definitions of risk is the degree that an asset swings in price. Because leverage amplifies these swings then, by definition, it increases the risk of your portfolio. b) A short sale allows an investor borrows a share of stock from a broker and sell it. Later, the short-seller must purchase a share of same stock in order to replace the share that was borrowed. This is called covering the short position. Example:
Profitable covered trade
Shares in C & Company currently trade at $10 per share. 1. A short seller investor owns 100 shares of C & Company and sells them for a total of $1,000. 2. Subsequently, the price of the shares falls to $8 per share. 3. Short seller now buys 100 shares of C & Company for $800, or alternatively, purchases 125 shares for $1,000. 4. Short seller retains as profit the $200 difference between the price at which he sold the shares he owned and the lower price at which he was able to repurchase the shares.
Loss-making trade
Shares in C & Company currently trade at $10 per share. 1. A short seller borrows 100 shares of C & Company and immediately sells them for a total of $1,000. 2. Subsequently the price of the shares rises to $25. 3. Short seller is required to return the shares, and is compelled to buy 100 shares of C & Company for $2,500. 4. Short seller returns the shares to the lender who accepts the return of the same number of shares as was lent. 5. Short seller incurs as a loss the $1,500 difference between the price at which he sold the shares he borrowed and the higher price at which he had to purchase the shares he returned (plus borrowing fees). Problem 3 a) S&P Average Return = 10.26, Standard Deviation= 17.89 % Range =97.79%

b)

c) Average of 1-year interest rate = %4.7033 Median = 4.62 Standard Deviation = 2.8004 Range =17.265

d) The correlation between 1-year interest rates and S&P returns is --0.0949496 which means that there it indicates that there is a slightly negative relationship between S&P returns and 1-Year interest rates.

e) E(r)= 4.47+((10.26-4.47)/17.8)Qc= 4.47+.325281*Qc Qc= standard deviation of portfolio E(r)= expected return of portfolio

f) Y= (E(r) – rf)/AQ^2 Y= the weight invested in risky asset

When A=.5 we have: Y=( .1026-.047)/(.5*.178^2)=3.509

It means this investor invest % 350.9 of his investment budget in S&P500 ( buy on margin(borrowing)).

When A=2 we have Y= .877414
It means that this investor invests % 87.74 of his investment budget in S&P500

When we have A=5 we have Y=.3509
It means that the investor invests %35.09 of his investment budget in S$P500.

Problem 4 | Small value | Small Growth | Big value | Big Growth | S&P500 | Average Return(Monthly) | 1.079 | 1.419 | .9072 | 1.083 | .855 | Standard deviation | 7.41 | 7.66 | 5.27 | 6.41 | | Sharp Ratio | 1.143 | 1.639 | 1.215 | 1.329 | |

S&P500 is used as benchmark for comparing absolute performance.
Absolute performance: Small Growth stocks has far higher average return than S&P500 (the difference is % 6.2 annually) .Big value firms has approximately same average return as S&P500.Big growth firm and small value firms have relatively higher average return than S&P500(the approximated difference is 3 percent annually).

Relative performance:
From comparing the sharp ratios it is concluded that small-growth companies had best performance. Big-growth companies are in next place. Moreover, big-value companies rank three. Finally, small-value companies had the worst performance

Small firms stocks have a higher average return than large cap stocks, because they have potential for growth, small firms have larger scope of growth as compared to large companies, but small firm have higher standard deviation because they are more sensitive to the change in the domestic and macroeconomics factors.
Moreover, the result indicates that value stocks average return is lower than growth stocks, moreover, they have lower standard deviation. Because growth companies have riskier nature, but value companied are less risky in their nature.