Derivative instruments and their role in modern economy

By,Ctlin Mihai Nstru

Under the guidance ofProf Jakub Keller

Content:1. Short description of the instrument 2. Info spot price, historical data3. Stock analysis Fundamental analysis Sentimental analysis Technical analysis Interpreting the results for 3 months Calculate the volatility of the stock using modern portfolio theory 4. Option chain Pricing the option using BSM Use of a simple strategy5. Results How investing in options is more profitable than buy and hold stock strategy6. Complex Strategy Strategy for bull market Strategy for bear market7. Conclusion

1. Short description of the instrument:Tesla Motors, Inc. (TSLA) designs, develops, manufactures, and sells electric vehicles and electric vehicle powertrain components. The company also provides services for the development of electric powertrain systems and components, and sells electric vehicle powertrain components to other automotive manufacturers. It markets and sells its vehicles through Tesla stores and galleries, as well as over the Internet. The company operates a network of 80 stores and galleries in North America, Europe, and Asia. Tesla Motors, Inc. was founded in 2003 and is headquartered in Palo Alto, California.[footnoteRef:2] [2: http://finance.yahoo.com/q/pr?s=TSLA+Profile]

On June 29, 2010, Tesla Motors launched its initial public offering onNASDAQ. The IPO raisedUS$226 millionfor the company.Tesla's strategy has been to emulate typical technological-product life cycles and initially enter the automotive market with an expensive, high-end product targeted at affluent buyers. As the company, its products, and consumer acceptance matured, it is moving into larger, more competitive markets at lower price points.[footnoteRef:3] [3: http://en.wikipedia.org/wiki/Tesla_Motors]

2. Stocks informationFigure 1 Source: http://finance.yahoo.com (06.01.2015)Annex 1: Historical prices3. Stock analysis

3.1. Fundamental and sentimental analysis

a. Financial ratiosCurrentYoY2010201120122013

SHARE VALUES

Earnings Per Share - TTM($1.12)495.52%($3.04)($2.53)($3.69)($0.62)

Dividends Per Share - TTM $0.00 $0.00 $0.00 $0.00 $0.00

Book Value Per Share$5.42 79.85%$2.18 $2.14 $1.09 $5.42

Free Cash Flow Per Share($1.10)364.67%($3.09)($3.86)($5.11)($1.10)

Sales Per Share$16.86 77.17%$2.30 $2.03 $3.85 $16.86

PROFITABILITY

Return on Equity (ROE)-18.6951115.44%-63.566-118.03-227.22-18.695

Return on Assets (ROA)-2.97961354.54%-39.762-46.271-43.34-2.9796

Gross Profit Margin22.6667.89%26.32330.1587.275622.66

Operating Profit Margin-3.04363034.73%-125.78-123.13-95.409-3.0436

Tax Rate

Interest Rate - Estimated Average6.003571.97%1.36631.83581.6836.0035

Net Profit Margin-3.67592508.23%-132.19-124.56-95.876-3.6759

ACTIVITY RATIOS

Total Asset Turnover0.8330855.48%0.302380.286270.37090.83308

Inventory Turnover4.766853.33%2.20432.63962.22464.7668

FINANCIAL RATIOS

Long-term Debt to Capital47.309-62.22%25.88854.75876.74247.309

Financial Leverage (Assets/Equity)3.6229-146.62%1.86473.18448.9353.6229

Fixed Charge Coverage Ratio-1.05654670.29%-154.4-49.364-50.398-1.0565

Dividend Payout (% of Earnings)00000

Quick Ratio1.330165.44%2.10211.63760.45971.3301

Current Ratio1.87548.09%2.75681.94860.97341.875

Table 1. Source: TD Ameritrade paperMoney - Thinkorswim trading softwareBased on financials we can observe a YoY increased sharply for every ratio, which can be translated into the company fast growing and a bet for bullish stocks. Yet we cant only buy stocks based only on the financial ratio, we need more information about the company.

Price / Earnings Ratio estimates[footnoteRef:4] Forecast Earnings Growth [4: http://www.nasdaq.com/]

b. Press releasedOn October 4, 2014, Tesla announced the 60D, 85D, and P85D dual-motor all-wheel drive variants of the Model S. The high-end P85D can accelerate from 0 to 60mph in 3.2 seconds and has a top speed of 155 miles per hour (249km/h).[footnoteRef:5] [5: http://en.wikipedia.org/wiki/Tesla_Motors]

On November 26, 2014 Tesla Motors announced the completion of upgrades to its Fremont, California factory.The Tesla Model X was unveiled at the company's design studios inHawthorne, CaliforniaFebruary 9, 2012. However, Tesla announced in February 2014 that in order to focus on overseas roll outs of the Model S during 2014, the company expects to have production design Model X prototypes by the end of 2014, to begin high-volume deliveries for retail customers in the second quarter of 2015. In November 2014 Tesla delayed one more time the start of deliveries to retail customers, and announced the company expects Model X deliveries to begin in the third quarter of 2015.On 4th September Teslas founder,Elon Musk, announce a project for $5 billion in wich is planning for building a facility as a key step toward making electric cars more affordable, while ending reliance on oil and reducing greenhouse gas emissions. The facility will produce high-voltage battery and will be entirely powered by renewable energy.[footnoteRef:6] [6: http://www.bloomberg.com/news/2014-12-05/musk-battery-works-fill-utilities-with-fear-and-promise.html]

Tesla said it lost $62 million in the second quarter, when they delivered 7,579 vehicles. The company says it's on track to deliver 35,000 cars by the end of 2014. A Tesla Model S retails for $71,070, according to the Tesla website.[footnoteRef:7] [7: http://www.businessinsider.com/r-tesla-factory-near-reno-is-bet-old-nevada-will-meet-the-new--2014-10]

On 18th February we expect annual financial report of the company, so we should take this in consideration when trading company.So, in order to asses better a company valuation we need to understand their products, services, and future projects. Based on some announces made by the company and the founder Elon Musk we can see that is planning to expand. Also we can see that the cars companys manufactures are in great demand by customers, and orders are rising. This can be a sign of company power and financial strength.3.2. Analyst Opinion sentimental analysisDateResearch FirmActionFromTo

17-Oct-14MLV & CoInitiatedBuy

08-Oct-14Tigress FinancialInitiatedNeutral

02-Sep-14StifelUpgradeHoldBuy

11-Aug-14Deutsche BankUpgradeHoldBuy

26-Mar-14UBSInitiatedNeutral

20-Feb-14Deutsche BankDowngradeBuyHold

19-Feb-14FBR CapitalInitiatedMkt Perform

07-Nov-13Standpoint ResearchUpgradeSellHold

02-Oct-13Robert W. BairdDowngradeOutperformNeutral

22-Aug-13StifelInitiatedHold

08-Aug-13BarclaysDowngradeOverweightEqual Weight

26-Jul-13Deutsche BankUpgradeHoldBuy

01-Mar-13Northland CapitalInitiatedOutperform

Table 2. Source: http://finance.yahoo.com/q/ud?s=TSLARecommendation Trends

Current MonthLast MonthTwo Months AgoThree Months Ago

Strong Buy3333

Buy101188

Hold5555

Underperform1111

Sell0000

Table 3. Source: http://finance.yahoo.com/q/ao?s=TSLA+Analyst+OpinionFrom the analyst point of view we can see that the recommendation is to buy and hold. Actually the company shares are forming an uptrend as we can see in the figure 1.Overall if we look on the fundamental analysis of the company we can see a strong bullish trend. But relying only on fundamentals and sentimental analysis is like we stay on a stool with only two legs. We risk falling and hurting ourselves. So we need to see what is happening at technical level.3.3. Technical analysisTechnical analysis is the framework in which traders study price movement.The theory is that a person can look at historical price movements and determine the current trading conditions and potential price movement.

Fibonacci Traders use the Fibonacci retracement levels as potentialsupport and resistance areas. Since so many traders watch these same levels and place buy and sell orders on them to enter trades or place stops, the support and resistance levels tend to become a self-fulfilling prophecy.Traders use the Fibonacci extension levels asprofit taking levels. Again, since so many traders are watching these levels to place buy and sell orders to take profits, this tool tends to work more often than not due to self-fulfilling expectations.I use a Fibonacci retracement in 1 year chart window, with a low of 136.67 and a high of 291.42, and for Fibonacci extension level I also use 17.12.15 lower level of 192.65. Annex 2

12

Fibonacci Retracement Levels0.236 - 252.880.382 - 230.440.500 - 212.310.618 - 194.180.764 - 168.36Fibonacci Extension Levels0 - 192.20.382 - 252.880.618 - 290.141.000 - 348.01

3.4. Interpreting the results

By using the Fibonacci retracement and extension levels I can analyze the past 3 months: 04.09.2014 we can see that in the beginning of the September the price has reached the maximum value 291.42, which is the 0.0 level of my retracement level.15.09.2014 we can see an downtrend after the maximum value until this date where 0.236 level acts like support and the price bounce back from 249.13, only is just for a short period, because on 22.09.2014 price pierce the 0.236 support level bringing the price lower as 235.65 on 01.10.2014. On this moment we can see a downtrend forming; we expect the price to fall even more. 04.10.2014 but on this date, Tesla announce new motors for the car Model S witch upgrade the performance of the car, and new orders for this car are availed and also the price meet the 0.382 support level, making the price of the actions rise again to maximum 265.54 on 09.10.2014. Now we can say its time to buy.10.10.2014 if we had bought a day earlier just assuming the price will rise due to the press released, we would have suffered hard, because in this date the market fall 187 points, and influence our stock, even if beta is lower than other public companies. Fortunately the 0.500 fib level holds, pushing the price back up from 217.32 on 17.10.2014. 17.10.2014 18.11.2014 in this time the market uptrend resumes moving our actions back again to 259.99 and we can see the 0.236 fib level acting like resistance pushing the price back again. 19.11.2014 Morgan Stanley lowered Tesla 2014 and 2015 earnings expectations, while leaving the target price unchanged at $320. Teslas 2015 earnings estimate have been reduced to $2.45 from the previous estimate of $4.39. Shares began a downward trend, being helped by the market which lost 100 points during 05.12.2014 15.12.2014, pushing our shares toward a lower of 192.62 on 17.12.2017, level that coincides with our 0.618 fib level. 18.12.2014 in this moment the market growth resumes, and we can see that our stock price starts to rise, breaking the 0.500 resistance fib level, but stopping their growth at 0.382 fib level to a maximum of 228.5 on 26.12.2014. Also this growth can be attributed to 10.12.2014 announcement in which is said that Tesla car registration in USA increased with 153% .01.01.2014 present we can see the 0.382 resistance fib level holds, and the price of stocks bounce back to the previous level, currently standing at the 0.500 fib level with a stock price of 206.75.For the first part of this year we can see the price fluctuates between 205-225 per share. We can expect the price to decrease, especially because will follow the financial report release on 18.02.2015, but we need to consider the other factors.

3.5. Calculate the volatility of the stockVolatility refers to the amount of uncertainty or risk about the size of changes in a security's value. A higher volatility means that a security's value can potentially be spread out over a larger range of values. This means that the price of the security can change dramatically over a short time period in either direction. A lower volatility means that a security's value does not fluctuate dramatically, but changes in value at a steady pace over a period of time.[footnoteRef:8] [8: http://www.investopedia.com/terms/v/volatility.asp]

a. Calculate historical volatility using standard deviation:The standard deviation essentially reports stocksvolatility, which indicates the tendency of the returns to rise or fall drastically in a short period of time. A security that is volatile is also considered higher risk because its performance may change quickly in either direction at any moment.[footnoteRef:9] [9: http://www.investopedia.com/articles/mutualfund/03/072303.asp]

I calculate standard deviation from historical price of the TSLA stocks with a timeframe of 2 and 1 and 0.5 years and the results are as follows based on Annex 1 excel calculation:HV (2 years) = 0.579644HV (1year) = 0.478902HV (0.5 year) = 0.414575Source: Annex 1: Excel sheet with calculationb. Calculate stock beta Determines the volatility (or risk) of a fund in comparison to that of its indexorbenchmark. A fund with a beta very close to 1 means the fund's performance closely matches the index or benchmark. A beta greater than 1 indicates greater volatility than the overall market, and a beta less than 1 indicates less volatility than the benchmark.[footnoteRef:10] [10: http://www.investopedia.com/articles/mutualfund/03/072303.asp]

Beta is calculated in excel using slope function:Beta = 1.831541Source: Annex 1: Excel sheet with calculationc. Calculate the stock alphaMeasures how much if any of this extra risk helped the stock outperform its corresponding benchmark. = Rp [Rf + (Rm Rf) ]Where:Rp= Realized return of portfolioRm= Market returnRf=risk-free rate = 1.9023%Source: Annex 1: Excel sheet with calculationd. Capital Asset Pricing Model CAMP

Using the CAPM model and the following assumptions, we can compute the expected return of a stock in this CAPM example: if the risk-free rate is 2%, the beta (risk measure) of the stock is 1.831541 and the expected market return over the period is 10%, the stock is expected to return 16.65% (2%+1.831541(10%-2%))

e. Sharpe Ratio The Sharpe ratio tells us whether a stock or portfolio's returns are due to smart investment decisions or a result of excess risk. The greater a portfolio's Sharpe ratio, the better its risk-adjusted performance has been.[footnoteRef:11] [11: http://www.investopedia.com/terms/s/sharperatio.asp]

If the risk-free rate is 2%, the standard deviation of the stock is 0.478902 and the expected market return over the period is 10%, the stock is expected to return 16.70% (10%-2%) / 0.478902.

Interpreting the resultsBased on the calculation, we can say that investing in Tesla stock is much riskier than investing in the S&P 500, but also is more rewarding. From the beta calculation we can see that movement in the S&P500 influence by 1.81 movements in TSLA stock, but also TSLA stock is more rewarding, beating the index return by 1.9023%. Using CAMP and Sharpe Ratio we can determine that an investment return must be above 16.65% for the risk worth taking.

4. Option chainBecause of the small amount of return and big capital requirements for investing in stocks and for hedging our risk we should look into the option chain for a smart investment strategy.I take the option chain for 27 days time frame with a strike price between 185-230, prices that coincides with 0,618 fib support level and 0.382 fib resistance level. I want to examine what would be the price of the options using Black-Scholes pricing model.

Impl VolProb.OTMDeltaBIDASKExp (days)StrikeBIDASKImpl VolProb.OTMDelta

43.54%19.50%0.8422.9525271852.53.247.45%78.19%-0.18

42.73%22.22%0.8120.8522.927187.52.93.4545.86%75.94%-0.2

41.84%25.17%0.7818.820.85271903.33.944.61%73.25%-0.23

44.56%30.32%0.74181927192.53.854.4543.73%70.10%-0.26

43.64%33.66%0.7116.117.15271954.455.2543.25%66.52%-0.29

42.84%37.28%0.6714.415.327197.55.25.9542.47%62.87%-0.33

42.11%41.13%0.6312.7513.62720066.941.99%58.91%-0.37

41.07%45.08%0.5911.1511.927202.577.841.40%54.84%-0.41

40.38%49.28%0.559.710.42720588.439.72%50.80%-0.45

40.11%53.60%0.518.59.0527207.59.39.8540.11%46.40%-0.49

39.37%57.92%0.467.17.92721010.411.439.81%42.12%-0.54

38.58%62.27%0.4266.6527212.511.7512.5538.70%37.76%-0.58

38.78%66.29%0.385.25.752721513.214.2538.56%33.64%-0.62

38.15%70.37%0.334.254.8527217.514.916.8540.67%30.55%-0.65

38.37%73.89%0.33.74.12722016.6517.4537.64%25.77%-0.71

38.57%77.13%0.263.13.5527222.518.3519.9538.75%22.96%-0.74

38.15%80.40%0.232.492.952722520.3522.440.25%20.70%-0.76

37.45%83.56%0.191.952.3627227.522.424.4540.48%18.10%-0.79

37.62%85.94%0.171.641.962723024.626.641.15%16.00%-0.81

Table2. Source: TD Ameritrade paperMoney - Thinkorswim trading software

4.1. Pricing the options using BSMThe Black-Scholes model is used to calculate the theoretical price ofEuropean put and call options, ignoring any dividends paid during the option's lifetime.

For pricing the options I will use Excel calculator, with a volatility (standard deviation) calculated earlier, of 0.478902, time to expiration 27 days, current stock price of 206.66, and a risk-free rate of 2%. The results will be:VolatilityDeltaCall valueDifference from marketStrikePut valueDifference from marketDelta

47.89%0.8229 $ 24.67 1.33%185 $ 2.74 15.52%-0.1771

47.89%0.7949 $ 22.75 0.66%187.5 $ 3.31 4.14%-0.2051

47.89%0.7648 $ 20.90 -0.24%190 $ 3.96 -1.53%-0.2352

47.89%0.7328 $ 19.14 -0.73%192.5 $ 4.69 -5.25%-0.2672

47.89%0.6993 $ 17.46 -1.79%195 $ 5.52 -5.01%-0.3007

47.89%0.6644 $ 15.88 -3.72%197.5 $ 6.43 -7.76%-0.3356

47.89%0.6285 $ 14.39 -5.65%200 $ 7.43 -7.40%-0.3715

47.89%0.592 $ 12.99 -8.76%202.5 $ 8.53 -8.95%-0.208

47.89%0.555 $ 11.69 -11.69%205 $ 9.73 -14.70%-0.445

47.89%0.5181 $ 10.48 -14.67%207.5 $ 11.01 -11.13%-0.4819

47.89%0.4814 $ 9.36 -16.96%210 $ 12.39 -8.33%-0.5186

47.89%0.4453 $ 8.33 -22.52%212.5 $ 13.86 -9.93%-0.5547

47.89%0.4101 $ 7.39 -25.09%215 $ 15.41 -7.83%-0.5899

47.89%0.376 $ 6.53 -29.74%217.5 $ 17.05 -1.18%-0.624

47.89%0.3432 $ 5.75 -33.82%220 $ 18.77 -7.29%-0.6568

47.89%0.3119 $ 5.05 -35.24%222.5 $ 20.56 -3.01%-0.6881

47.89%0.2822 $ 4.42 -40.43%225 $ 22.43 -0.13%-0.7178

47.89%0.2543 $ 3.85 -48.94%227.5 $ 24.35 0.41%-0.7457

47.89%0.2281 $ 3.35 -53.60%230 $ 26.35 0.94%-0.7719

Table2. Source: Own calculations in ExcelIf we are to invest using Black-Scholes model, we would buy underestimated options and sell over evaluated options compared with the market, and assume the price will go in our direction. According to this model the volatility (stand.dev.) must remain constant for the model to work, and the model does not include some technical factors as liquidity, supply and demand, that can influence the price.From the table we can see that the market underestimate call options with strike prices above 210, and put options with strike price between 205- 212.5 and if weve buy them it seems the price will turn in our favors. Another interpretation is that the market is expecting the price of underlying asset to decrease and thats why the high strike price of call options is under evaluated. But only to buy and hold a call/put option hoping to go in the right direction, based only on BSM is not a good strategy.

5. ResultsAccordingly to CAMP model and Sharp Ratio, our buy shares of TSLA Company, are returning approximately 16% annually, which is much better than bonds and bills, but considering the risk is fair enough.Weve seen that TSLA stock have a high volatility and in this case are better to hedge our self with options. One way to do this is o buy a put option just in case the price will decrease. Based on my technical analysis, it seems that the price of the stock will decrease, so it is always a good choice to insure our risk. And since weve bayed the stock is always a good idea to make some additional money selling OTM options. And one way to do this is selling covered calls and making a profit from the premium received. In this case we hope the stock price will stay flat or go down and the option would expire worthless.Formula: Buy 100 shares of TSLA at the price of 206.66 (100*206.66 = 20.666$) Sell one 215 call option with expire day of 2015-02-07 (27 days) for 5.2 Buy one 190 put option with expire day of 2015-02-07 (27 days) for 3.9 Max reward = 215 206.66 + 5.2 3.9 = 9.64 * 100 shares = 964 $ when the price of the underlying asset is 215 Max risk = 206.66 215 + 5.2 3.9 = 7.04 * 100 shares = 704 $ when the price of the underlying asset is 190$In this case we pay 20.666$ for long 100 stock and receive 130$ in premium for this collar strategy. In this scenario we have 3 posibilities:1. TSLA shares will stay below 215 call strike price and the option will expire worthless and we keep the premium, and outperform the stock2. TSLA shares fall call option will expire worthless and we keep the premium and outperform the stock, and we are protected against a decline below 1903. TSLA shares rise above 215 the option is exercised and my upside is capped at 215 + option premium. In this case, if the stock price goes higher than 215 plus the premium, our collar strategy will underperform the TSLA stock.

6. Complex strategyFor this type of market my complex strategy will use a vertical spread, which involves 2 contracts, one buying option and one selling option of the same type and expiration, but a different strike. Also for this kind of transaction I dont need to buy the stock, decreasing the amount of capital needed.

a. For a bull marketFor call options: strategy name bull call debit spread Current price = 206.66 Buy a 200 call option for 13.60 Sell a 207.5 call option for 9.05 Payment 13.60 9.05 = 4.01 * 100 shares = 401 $ Max reward = (207.5 200) * 100 shares = 750 401 = 349$ for a price above 207.5 Max risk = 401 $ for a price lower than 200 Breakeven point = 200 + 4.01 = 204.01For put otions: strategy name bull put credit spread Current price = 206.66 Sell a 207.5 put option for 9.3 Buy a 195 put option for 5.25 Max reward = 9.3 5.25 = 4.05 * 100 shares = 405 $ if the price is above 207.5 Max risk = (207.5 195) *100 405$ = 845 if the price fall under 195 Breakeven point = 207.5 4.05 = 203.45

b. For a bear marketFor call options: strategy name bear call credit spread Current price = 206.66 Buy a 215 call option for 5.75 Sell a 205 call option for 9.70 Max reward = 9.70 5.75 = 3.95 * 100 shares = 395$ if the price is under 205 Max risk = (215 205) * 100 395 = 605 $ if the price rise above 215 Breakeven point = 205 + 3.95 = 208.95For put options: strategy name bear put spread Current price = 206.66 Buy a 212.5 put option for 12.55 Sell a 205 put option for 8.00 Payment = 12.55 8.00 = 4.55 * 100 shares = 455$ Max reward = 212.5 205 = 7.5 * 100 shares = 750$ - 455 = 295$ if the price is under 205 Max risk = payment for the options = 455$ Breakeven point = 212.5 4.55 = 207.55

7. Conclusion:

In conclusion, I can say that there are hundreds of option strategies that can limit our risk, but in order to take advantage of the full power of options trading, we need to have a big trading account. One the best thing in these strategies is that we can calculate before transaction our risk/reward ratio, and invest accordingly to our adversity towards risk. Another thing o take into account when we decide to invest in options is our timeframe (time decay), and we can make profit only by speculating on a short term the direction of the underlying making a good amount of return.Usually traders use a margin account, which have a limited buy power, and bigger B/P effect than a IRA account. But an IRA account cost from 25.000$ and beyond. For a margin account we can still use a lot of different trading strategies, we can open positions when we want and how many we want and the account permitted. One thing when we open an account is to take into account the broker fees and commissions for transactions. I didnt include them into my strategies, and these costs are affecting our profits.Also for just investing in a portfolio of stock, we can use modern portfolio theory for assessing our risk/reward ratio and use a strategy like diversify our portfolio. Best when we choose to invest in stock is to have a view in a long/medium time period. As we can saw in this analyze, TSLA stock will offer us a much better return in long term than bonds, and bank deposit do.

Bibliography:

1. http://finance.yahoo.com/2. http://www.investopedia.com/3. http://en.wikipedia.org/wiki/Tesla_Motors4. http://www.theoptionsguide.com/5. https://www.youtube.com/watch?v=BZyfXsL-maM6. http://www.babypips.com/school/7. TD Ameritrade paperMoney - Thinkorswim trading software