Derivative Securities and Risk Management Techniques - Assignment Example

DERIVATIVE SECURITIES AND RISK MANAGEMENT TECHNIQUES: QUESTION ANALYSIS by ( Student’s Name) Course Name + Code Professor’s Name Date of Submission Derivative Securities and Risk Management Techniques: Question Analysis Part1) Hedging with Futures: Hedging Strategy and Its Implementation 1. Using the Futures It is noted that both the upside and downside risks can be eliminated or reduced by the employment of long and short-term hedges, the elimination of the upside risk is actually considered to be a hindrance in the course of hedging using the futures (Hyer 2010). Short Hedges A short hedge is defined as a hedge in which a short position is deployed on a contract of futures (Hyer 2010). Whenever there is an expectation that an asset is going to be sold in the future, then, the best strategy is to use a short hedge. Secondly, it can be employed by a speculator who anticipates that the contract price is likely to decrease in the future. For instance, assume that an investor plans to sell an asset in November and basing it on the at the time’s spot prices, then the investor can use the following hedging strategy. At the moment, A November future contract currently is being purchased at a price of $1220 To simplify, an assumption is made that the investor anticipates selling and actually sells worthy $10,000; this is tantamount to a single contract. The spot prices are stated at $1220 The question that lingers is; what then happens in November when the spot prices decreases to $1210? In this regards, the investor will be losing $10 for every 1000 dollars from the reduced selling price. The investor gains $10 out of selling at a price of $1220 future contract and selling to close out immediately at the price of $1210 Another question that requires a good strategy is what will happen in November should the spot prices increase to $1230? Then the investor will gain $10 per 1000 dollars from the increased price on the sale The investor will likely lose $10 whenever he buys the futures contract for $1230 and then, having it sold to a close price of $1230. This will be construed to mean that the seller has efficiently, prior to the sale, locked in on the price by offsetting the losses and gains. 2) Thus, if it is assumed that the same speculator takes on the November futures contract at the price of $1220, and should the price fall to $1210, then, the speculator will have to sell for $1220 and immediately, purchase at $1210, and this will give the investor a gain of $10 within a single contract. On the other hand, should the price increase to $1230, then, the speculator will lose $10. Long Hedges This is a situation whereby, on a futures contract, a long position is assumed hence this is called a long hedge. It is the best strategy that can be employed in these circumstances in case the investor wants or expects to invest in the future. The strategy is best used by a speculator who highly anticipates for future price rise. To give an example from the data given, supposing that an investor wants in the month of November to purchase stock at a price that is equivalent to the spot price at that time. Then, the stock market can hedge in the manner explained below from the given information; A November stock purchases stock futures contract goes at the price of $1194.91, the current spot prices are $1195.91, then the question to answer is on what will happen in November should the prices decrease to $1190.91? Then the seller will gain $4 per stock purchased upon the decreased price. Subsequently, the seller will lose $4 through the purchase of the futures contracts for $1191.91 and then selling them to a close of $1190.91. Thus, the sale effective price is $1191.91 What will happen should the November spot price increase to $1195.91? The seller will lose $6 on each stock out of the increased price. Sellers in the market will gain $6 from the sale of the futures contract for selling at the price of $ 1190.91 and then buying to close immediately at the price of $1194.91. This means that the seller, in this case, has used a strategy to effectively lock in on the price earlier on before the sale. This is greatly affected by offsetting losses /gains. Trading Strategies by the Use of Options This case can, as well, employ trading strategies with the use of options. This is possible due to the following aspects; The investor needs to take a position in the underlying stock, then, conduct a spread by taking position 2 of the same type. For example, bear, bull, butterfly, diagonal, box and calendar and then, lastly, through combinations whereby an investor might assume a position in a calls and puts mixture that might include; straddle, straps and strips. Estimation of the Hedge Ratios Let assume that the period at the moment is t – 1and the period hedged to determine the ratio is y t. then f t – 1 is the price of the futures at t – 1 The hedge ratio is determined by the formula covariance (change in y, change in x) / variance change in x Assuming the constant variance and covariance, given the standard deviation б = 0.1840812 then variance is 0.18408122 = 0.034. Taking the 76/100, the targeted change in y, change in x, thus, the hedge ratio = (change in y, change in x) / variance change in x =0.76 / 0.034 = 22.35 Calculation of the Number of Contracts In the futures market, the number of contracts is the size of the trade. The minimum number of contracts is one. It should be noted that tick value, stop loss size and the maximum risk acceptable are used in determining the number of contracts Number of contracts = 200 / 5 /6.50 = 6(rounded off to whole contracts) With the change of the index following the weekly rebalancing of the portfolio, the new number of contracts will be 200 / 4 / 4.50 = 11(rounded off to whole contracts) Trading Strategies That Involve Options This strategy can also be used; it entails assuming a long position in a futures contract and a subsequent call option for a short position. The investor is covered from the pay-off by conducting a short call writing that is termed to be necessary should the prices increase within due the long position. Should the prices drop, then, the downside risk will persist. Part 2: Trading Options The stock with more than 10 billion market capitalization chosen is Cisco Company with a $ 15 billion market capitalization; the following is a summary of the company and its market news. Targeted price summary Targeted mean 26.68 Targeted median 28 Highest target 32 Lowest target 16 Number of brokers 33 Company’s History on both the Upgrades and Downgrades Date Required action To From 15, August 2013 Upgrading neutrality Cautious 30, September 2013 Upgrading Market average performance Underperformance 21, March 2013 Down grading Underperformance Market average performance 12, March 2013 Down grading Holding Buying 14, February 2013 Initiating Outperformance 14, January 2013 Upgrading Outperformance Neutrality 3, January 2013 Upgrading Outperformance Sector average performance 17, October 2013 Down grading Holding Buying 2, October 2013 Upgrading Buying Neutrality 10, August 1013 Initiating Holding Recommendation Trends; Three months ago Two months ago Last month Current month Strong buy 10 11 11 8 Buy 21 18 15 17 Hold 9 9 12 12 Underperformance 6 4 2 3 Sell 0 0 0 0 The second Company that is considered is Applied Materials Inc. (AMAT) Company whose market capitalization stands at $8 billion. Targeted price summary Targeted mean 19.46 Targeted median 19.76 Highest target 21.00 Lowest target 12 Number of brokers 17 History on upgrades and down grades Date Required action To From 28, August 2013 Initiating outperformance 30,september 2013 Upgrading Buying Neutrality 22, March 2013 Down grading Neutrality Buying 20, March 2013 Down grading overweight Equal weight 15, February 2013 upgrading Holding Buying 14, January 2013 Upgrading Outperformance Performance of the sector 3, January 2013 Downgrading Equal weight Overweight 29, October 2013 Initiating Holding 5, October 2013 Initiating Average performance 17, August 1013 Upgrading Overweight Equal weight Recommendation Trends; Three months ago Two months ago Last month Current month Strong buy 3 3 3 4 Buy 7 6 7 8 Hold 8 8 2 7 Underperformance 5 4 4 3 Sell 0 0 0 0 The third stock to be analyzed is of the company Caterpillar Inc. (CAT) with a market capitalization of $1 billion. Targeted price summary Targeted mean 92.28 Targeted median 92 Highest target 1.6 Lowest target 76 Number of brokers 21 History on Upgrades and Down Grades Date Required action To From 18, August 2013 Upgrading neutrality Outperformance 1320,May 2013 Initiating Sector average performance 11, March 2013 Down grading Neutral Out performance 16, March 2013 Down grading Buying Buying 12, February 2013 Initiating Overweight Neutrality 10, January 2013 Initiating Buying 12, January 2013 Upgrading Outperformance 12, October 2013 Initiating Outperformance Neutrality 2,1 October 2013 Upgrading neutrality 101 August 1013 Initiating Holding Selling Recommendation Trends; Three months ago Two months ago Last month Current month Strong buy 5 5 4 3 Buy 11 11 9 9 Hold 9 9 9 11 Underperformance 0 0 0 0 Sell 0 0 0 0 Two-Option Trading Strategies The two-option trading strategies are a type of marketing-strategy that acts on neutrality concept. This makes it possible for the traders in the market to earn a profit from virtually all market conditions that were available at that moment. These conditions are side trends, up trends and downtrends movements. This strategy has further been categorized into convergence trading and statistical arbitrage strategy. The strategy keeps a look at any two but historically correlated securities. For this case, the historically related securities are the Cisco that has a stock market capitalization of about $15 billion and AMAT whose stock market capitalization stands at $ 8 billion. It has been noted that at times, the correlation between the two securities sometimes weaken, that is, at times whenever Cisco moves up, AMAT, moves down and vice versa. The two-option strategy would be to have the outperforming stock shortened and to have the underperforming stocks lengthened. The bet, in this case, as all this continue is to have two stocks converge at some moment in time. It should be noted that this temporary divergence is caused by a temporary demand and supply differences and also, such market changes as large purchase of one security and good information acquired by the speculators within the market, which showcases a possibility of sudden increased demand. Example Analysis Cisco and AMAT are two stocks from different companies, which manufacture similar products. The two companies have, historically, shared similar highs and lows. However, this has greatly been contributed by the individual company performance and inherent market risks. In the case that the market of Cisco is likely to increase and thus trade highly by an amount that is significant, while that of AMAT remains the same, then a two-option strategist would buy AMAT and sell Cisco, then assuming that both Cisco and AMAT prices will get back to their historical balance point; that is, if the price of AMAT rose to close the price gap that was created. For this case then, the investor will make a profit on the stock of AMAT. On the other hand, in cases the Cisco stock-price fell, the investor will still make money on having assumed a shortened Cisco stock. b). Strategy Implementation and Calculation of Loss as at September 30, 2013 It should be noted that should the entire market crash and the result being that the two stocks plummeting along with it, that is, the spread is characterized by a trend instead of a revert to the original position , then, on a short position, it will result to a subsequent gain and a loss Cisco made a loss of; (22.78 -11.27) x 14,649,724 =$1,686,183 c) Profits and Losses on the Closed Position as at October 11, 2013 Profits for Cisco Company; (0.73 x 0.52% = 0.003796) x 14, 649, 724 = $ 55,610 It should be noted that the company did not make any loss at this time. d) The strategies are effective as the investors and market speculators can use it to make more money whenever there is existence of a spread in the stock-prices. The strategies work best whenever stock prices are able to strike a balance point within the historical prices. Part 3) Volatility Estimation It is important to realize that investors, dealing with stock money, are interested in knowing the amount of risk or volatility that they are exposed to. This is because, volatility will aid in determining the range that stocks are likely to be placed in respect to their relative values. Having the ability to determine the range of volatility that an investor can face at any given time, then, such an investor is able to control the direction of their respective investments by making informed decisions. It should be understood that volatility determines the range of the values of an asset in terms of price and the level of its mean for any given fixed amount of time. Therefore, volatility is connected to the asset price fluctuations. Should a stock be referred to as volatile, then the stock price will vary to a greater extent over time. On the other hand, a stock that is less volatile will have its prices not being deviated greatly. Historical Volatility In order to determine the historical volatility, the following formula will be used; R 1 =In(s i / s i - 1) It should be noted that the money, which is continuously compounding like in the case of 250 stocks, is an exponential function. Then, the stock values from s 0 – s 250 must be generated hence resulting to a simulation result of 250 returns values. That is R 1 –R250, and then, the historical volatility will be found by computing the values of the average returns; R 1 = 1 / n ∑ R I, where n is the number of returns, that is 250 in this case. The standard deviation will be used in volatility estimation. Б = 1 /d t 0.5 1 /n – 1 ∑ (R 1 – R mean) 2 The estimated volatility for the 250 returns is Б = 0.1840812 b) Historical Volatility Estimation Using Entire Stock Price Series Trial Continuous Discrete Trial 1 20.5682 20.6386 % Trial 2 18.2583 % 18.3526 % Trial 3 19.2653 % 19.1253 % Trial 4 19.3568 % 19.2136 % Trial 5 19.4582 % 19.3623 % Trial 6 19.2562 % 18.3523 % Trial 7 18.2325 % 18.3325 % Trial 8 19.3256 % 19.2546 % Trial 9 20.2365 % 19.3523 % Trial 10 19.2556 % 21.2325 % Trial 11 21.3265 % 21.3254 % Trial 12 21.2365 % 19.1236 % Trial 13 19.2356 % 21.1326 % Trial 14 21.2365 % 21.1356 % Trial 15 23.3652 % 23.2325 % Trial16 20.1232 % 2.21253 % In the above table, the columns contain estimates from both the continuous and discrete methodologies. It should be noted that both of these methods; discreet and continuous, display results that are relatively close to one another. For each of the method, the volatility does not deviate for more than 1.5 %. Volatility Estimation Using the First Series Trial Continuous Discrete Trial 1 21.4682 % 21.6386 % Trial 2 19.1583 % 1.3526 % Trial 3 18.1653 % 18.1253 % Trial 4 17.1568 % 17.2136 % Trial 5 18.2582 % 18.3623 % Trial 6 18.3562 % 18.3523 % Trial 7 17.1325 % 17.3325 % Trial 8 18.256 % 18.2546 % Trial 9 20.22365 % 20.3523 % Trial 10 19.1556 % 19.2325 % Trial 11 31.2265 % 31.3254 % Trial 12 21.2365 % 21.1236 % Trial 13 19.3356 % 19.1326 % Trial 14 21.2365 % 21.1356 % Trial 15 13.2652 % 13.2325 % Trial16 16.2232 % 16.21253 % Volatility Estimation Using the Last Stock Series Trial Continuous Discrete Trial 1 21.5688 % 21.636 % Trial 2 19.2535 % 12.23352 % Trial 3 18.365 % 18.45125 % Trial 4 17.7535 % 17.7816 % Trial 5 18.882 % 18.6234 % Trial 6 18.5567 % 18.3234 % Trial 7 17.3325 % 17.4535 % Trial 8 18.2564 % 18. 2478% Trial 9 20.8352 % 20.4526 % Trial 10 19.9568 % 19.5563 % Trial 11 31.7254 % 31.4724 % Trial 12 21.6359 % 21.1675 % Trial 13 19.7356% 19.2624 % Trial 14 21.9355 % 21.576 % Trial 15 13.4552 % 13.2555 % Trial16 16.4452 % 16.53 25% From the above tables, it can be noted that volatility is close to each other, this is the case for the both discreet and the continuous methods for all the stock series computed from the above three examples. D) Historical Volatility and the Current Implied Volatility It is been noted that there is no much big difference or deviation between the historical volatility and the current implied volatility. The differences can only arise in cases where there are major changes within the underlying market. For the changes to cause a major volatility change between the stocks, it means that there has been an industry specific risk that has affected the stock under discussion (Kolb & Overdahl 2003). References List Hyer, T. 2010. Derivatives algorithms; Volume 1, Singapore, World Scientific. http://public.eblib.com/EBLPublic/PublicView.do?ptiID=731277 Kolb, R. W., & Overdahl, J. A. 2003, Financial derivatives, Hoboken, N.J., John Wiley, http://public.eblib.com/EBLPublic/PublicView.do?ptiID=152011 Read More