Equity Portfolio November 25, 2013 BUS 421

Transcription

1 Equity Portfolio November 25, 2013 BUS 421 Group 3 Robert Cherry Ara Kassabian Shalina Singh Kyle Thompson

2 I. PORTFOLIO INSURANCE The level of portfolio insurance we used was 5% (the default), which means the equity portfolio is protected against a 5% decline in value in the case of a bearish market downturn. Also, and we analyzed S&P 100 (^OEX) index options with a strike price of $745 and an expiration date of December 6, Two put contracts were needed to construct this hedge. There was a 0% decline in the value of the portfolio, so the portfolio insurance was not needed. Hence, the net payoff was $-246, which was the premium paid for the insurance. The current value of this insurance is $ and it covers the portfolio for up to $7,570 of loss coverage and $ of downside insurance. In addition the loss-coverage ratio is -0.03, which represents the price of premiums paid relative to the amount of insurance coverage received (-$246/$7,570). II. EQUITY PORTFOLIO: MACRO HEDGE WITH INDEX OPTIONS Six option strategies based on S&P 100 (^OEX) index options were analyzed, including: 1. Bull Call Spread 2. Long Call Butterfly Spread (recommended) 3. Long Straddle 4. Long Gut 5. Short Put Condor 6. Collar All strategies are described in further detail below as well as a detailed definition of the computed Black-Scholes Greek terms. In addition, total profit graphs are displayed for each strategy. 1

3 a. Bull Call Spread This strategy requires buying one ITM 785 call and selling one ITM 795 call. Both profit and loss are very limited, and the upper and lower bounds are clearly established. Profit in this situation is limited to the difference between the strike prices, net of premiums. This strategy seems plausible when anticipating a short-term increase in the value of the underlying. 2

4 b. Long Call Butterfly Spread This strategy requires buying one ITM 785 call contract, selling two ITM 795 call contracts, and buying one OTM 805 call contract. High profit would occur when the price is between the body of the butterfly at expiration. The maximum profit is limited to the difference between the two middle calls, net of premiums and the maximum loss is equal to total premiums paid to enter the position. Although minimal in certain situations, there is profit potential no matter which way price moves. However, when price is between $778 and $806 there is a large potential profit to be made. Spot price for the underlying is currently $796.32, and there is a wide space between the wings and body, which shows a potential for major profits. The long-call butterfly spread is an appropriate low-cost strategy for a stock trading in a narrow range or direction-neutral Therefore, this strategy is highly recommended. 3

5 c. Long Straddle This strategy requires buying one ITM 785 call contract, and buying one OTM 785 put contract. Volatility is very important when choosing this strategy. When the underlying s price either increases or decreases beyond either BEP, a profit is realized. Maximum profit is the difference between the underlying s price and strike price, net of premiums paid for both options. However, roughly a $17 increase (2.1%) or $37 decrease (-4.6%) in the underlying s price is needed to make a profit. Although this strategy could potentially be profitable in a volatile market, we do not anticipate this much volatility within the next four weeks. Therefore, this strategy is not particularly recommended. 4

6 d. Long Gut This strategy is similar to that of the long straddle as previously discussed. Roughly a $31 increase (3.9%) or a $23 decrease (-2.89%) in the underlying s price would be necessary for this strategy to make a profit. Since we do not anticipate this much volatility within the next four weeks, this strategy is not particularly recommended. 5

7 e. Short Put Condor This strategy requires selling one OTM 785 put contract, buying one OTM 795 put contract, buying one ITM 805 put contract, and selling one ITM 815 put contract. Profit and loss are both capped at $5, and a greater chance for profit occurs when price declines. Therefore, this strategy is not particularly recommended at this time. 6

8 f. Collar This strategy requires buying one OTM 815 call contract, and selling one OTM 785 put contract. Profit is seen only in a bullish market. This is a very risky strategy, and in the case of a bearish market, losses can be very high. A $19 (2.39%) increase in price is needed to generate profits. This strategy is potentially profitable, but not particularly recommended. 7

9 Greek Terms Analysis Option Intrinsic Price Hedge Theta Gamma Vega Rho Implied Volatility Call Call Call Call Put Put Put Put ITM 795 Call Delta- is the hedge ratio for a delta-neutral portfolio. Delta is This means that we should sell 1,000 OEX index call options for every 826 shares of the underlying purchased. This would be the optimal hedge ratio. Gamma- measures the effect of changes in the underlying with respect to the rate of change of delta. Gamma is If the underlying s spot price changes, delta must be adjusted to maintain a deltaneutral portfolio. For example, if price rises from $ to $797, then the new delta would be computed as follows: ( )(0.1823) = Therefore, we would have to purchase an extra 124 shares of the underlying ( = x 100) to maintain a delta-neutral position. Theta - measures the effects of passage of time. Theta is A change in expiration time has an impact on an options price, or premium. For example, if time to expiration changes from 30 days to 20 days, then the new price is computed as follows: [ ( )( )] = $ As options get closer to expiration, their price goes down. Vega measures the effects of volatility. Vega is A change in Vega affects the price/premium of the option. For example, if volatility increased from 15.53% to 18%, then the adjusted price would be computed as follows: [ ( )(58.645)] = $ A spike in volatility increases the price of options. Rho measures the effects of interest rates. Rho is = A change in interest rates affects the price/premium of a call. The current interest rate is measures at 0.00%. If the interest rate increases to 0.01%, then the adjusted price would be computed as follows: [ ( ) ( )] = $ IV Implied volatility is approximately 15.53% for this call option. A jump in volatility increases options prices. In addition, implied volatility is lower for NTM options. 8

10 Call implied volatility is consistent with a smile. As opposed to NTM options, ITM and OTM options have higher volatility. Volatility appears to be higher for OTM calls as compared to ITM calls. Also, volatility is higher for options that are closer to maturity. 9

11 Put implied volatility is consistent with a smile. Demand for deep ITM and deep OTM put options are much higher than NTM options. Volatility appears to be higher for ITM puts as compared to OTM puts. Also, volatility is higher for options that are closer to maturity and volatility is also at its deepest point at NTM options 10

12 III. EQUITY HEDGE: STOCK INDEX FUTURES HEDGING The market index chosen is the S&P 500 Index. The chosen futures contract is the E-Mini S&P 500. This contract is linked to the S&P 500 Market Index by a multiplier of 50. The correlation coefficient (Corr. P,I), which shows how correlated the portfolio is to the market index, is This means the portfolio is closely correlated to movements of the chosen market index. The diversity of our portfolio is similar to that of the S&P 500 market index. A diversified portfolio reduces risk and it also maximizes returns. Since the S&P 500 contains stocks from various industries, we deemed it appropriate to link a diversified portfolio to a diversified market index. In addition, the portfolio s beta is close to 1.00, which shows it will tend to move in the direction of the chosen market index. Our portfolio has a beta of 1.14, which means is the portfolio is 14% more volatile than the market as a whole. With this higher beta come higher rewards but also higher risk. This portfolio may outperform the market when it is bullish, but may also underperform the market when it is bearish. a. Portfolio Back-test A portfolio back-test was performed starting on September 23 rd and ending November 20 th. 11

13 On September 23rd, the market price is reported at $1, The next trading day, the market displayed bearish behavior by falling to $ Therefore, this dynamic hedge will execute the minimum variance hedge ratio. Then, a futures hedge was opened by selling two contracts. Then on September 25 th the market continued to fall down to $1, It was expected that the market will display bullish behavior, and on the next day the price was $1, In effect, the hedge was closed out by buying back two of the same contracts that were previously sold on September 23 rd. The closing price on September 27 th was indeed higher, and the portfolio realized a profit of $700. Overall, the portfolio experienced a $590 increase in its net position over the look-back period and a positive net change in wealth of $16,

14 b. Market Tracking Charts With a beta of 1.14, this portfolio experienced higher volatility as compared to the market index. In times of bullish behavior, the portfolio may outperform the market index. However, in times of bearish behavior, the portfolio may underperform the market index. With this higher risk comes higher reward. In late September, the market displayed signs of bearish behavior. As the market started to go down, the value of the portfolio decreased more than the index. However, in early to mid-october, the market became bullish and the portfolio and market index were moving together in unison. As the market stayed bullish during the coming weeks, the portfolio outperformed the value of the market index. 13

15 The chart above gives the audience a visible explanation of how essential it is to hedge a portfolio; in this case this chart is an example of this particular portfolio. With an unhedged portfolio our losses are uncapped as opposed to a hedged portfolio. 14

16 Here our hedged portfolio graph shows our profits are moderately increasing. Even in an extremely volatile market our portfolio s hedge seems to work as forecasted. Though the indexed value was higher on November 20 th than the portfolio s value, it was still profitable. 15

17 In early October, the Bollinger Bands were very wide. Therefore, volatility is high and prices vary. Thus, a profit can be made off price increases and decreases. There is a period of contraction in late October, which may be an indicator of future expansion and possibly high volatility in the coming days. As predicted, an expansion is seen in mid-november. It appears that another contraction may come in the next week. 16

18 c. Average Return, Standard Deviation, and Risk-Adjusted Performance Measures The average return on the portfolio was 0.26% and the average return for the market index was 0.08%. The portfolio deviation was 0.97% and the market index deviation was 0.70%. This shows that the portfolio s average return was centered further from the mean than that of the market index. The skewness for the portfolio was 0.12, and the skewness for the market index was In effect, the portfolio s returns were closer to a normal distribution than that of the market index. The Sharpe ratio was for this portfolio and for the market index. Since the ratio is higher for our portfolio as compared to the market index, there is great benefit in investing in this portfolio. For every unit of risk taken on by the portfolio, more return was received. The Treynor Measure for our portfolio was 0.83 and 0.29 for the market index. This is beneficial because the portfolio obtained an excess return of 0.83 for every unit of systematic risk. VaR for the portfolio was 1.65% and 1.29% for the market index. This is undesirable because the portfolio VaR is higher than the market index. This means that on any given say, we can say with 99% confidence that the portfolio has a 5% chance of losing $2, as compared to a 5% chance of the market index losing $23.05 on any given day. CVaR for the portfolio was 2.53% and 1.71% for the market index. This means that on any given day, we can say with 99% confidence that the portfolio has a 1% chance that the daily loss would exceed $4, Also, the market has a 1% chance of losing $30.04 on any given day. 17

19 Omega for the portfolio was 1.46 and 1.12 for the market index. This can be interpreted as for every 1% change in the underlying s price, the price of the call option will increase by 1.46%. Sharpe-Omega for the portfolio is 0.40 and 0.11 for the market index. d. Final Report Market Summary Ticker Symbol Year High Year Low EPS / Bid / Fx PE / Ask / YTD Return (%) / Close Qty Current Yield Market Capitalization / Net Assets / Stock Price Number of Shares Outstandi ng ('000) Beta V_Beta ENCO $ $ $(2.39) % $ ATTD $ $ $(0.69) % $ KLIC $ $ $ % $942,500,000 75, HIW $ $ $ % $3,262,000,000 89, DHI $ $ $ % $6,174,000, , IRBS $ $ $(0.34) % $ PSX $ $ $ % $41,110,000, , JGBO $ $ $ % $ LPHI $ $ $(0.12) % $34,300,000 18, FTTN $ $ $(0.12) % $9,100,000 9, RBCN $ $ $(0.72) % $230,700,000 22, TXI $ $ $ % $1,668,000,000 28, CMSB $ $ $ % $14,300,000 1, GFI $ $ $ % $2,935,000, , GIGA $ $ $(0.84) % $5,500,000 5, BGVF $ $ $ % $ HITR $ $ $(0.01) % $3,000,000 75, JHI $ $ $ % $161,000,000 8, NECB $ $ $(0.09) % $89,000,000 12, HRAA $ $ $(0.10) % $14,500,000 54, RYUN $ $ $(0.16) % $5,600,000 59, RVUE $ $ $(0.04) % $12,700, , HPY $ $ $ % $1,606,000,000 36, SNRV $ $ $(7.21) % $ CURRENT TOTALS

20 Portfolio Status Ticker Symbol Price Paid / Recv QTY Current Value: Managed Portfolio Weight Gain Over Base ENCO $ $ % $(7.50) ATTD $ $ % $(0.30) KLIC $ $6, % $(74.00) HIW $ $18, % $ DHI $ $9, % $ IRBS $ $ % $0.00 PSX $ $34, % $1, JGBO $ $ % $(0.00) LPHI $ $ % $(94.00) FTTN $ $ % $(20.00) RBCN $ $5, % $(75.00) TXI $ $29, % $1, CMSB $ $4, % $60.00 GFI $ $1, % $(222.50) GIGA $ $ % $(50.00) BGVF $ $3, % $(0.00) HITR $ $ % $7.35 JHI $ $9, % $(220.00) NECB $ $3, % $(259.00) HRAA $ $ % $5.00 RYUN $ $ % $7.45 RVUE $ $ % $7.70 HPY $ $21, % $(75.00) SNRV $ $ % $(2.50) CURRENT TOTALS $148, $148, % $2, BEGINNING Value $146, $146, $2, Overall, while options give the buyer the right but not the obligation to exercise, futures contracts require both parties to execute the transaction regardless of whether the contract is profitable or unprofitable. We would prefer options over futures because they have great leveraging power which makes them cost efficient. Options offer less risk, more investment alternatives, and higher potential returns. 19

21 IV. AUTOMATED TRADING a. Portfolio Summary The current year ROR for the buy-hold strategy is 0.90% and -6.40% for the automated trading strategy. However, this Automated Trader only displays only 8 out of the 23 stocks in the portfolio. Therefore, it is difficult to determine the true current ROR due to a time delay for the Automated Trader in displaying all of the portfolio s stocks. In addition, the ROR starting on the date of the simulation period (June 1, 2009) was 23.15% for the buy-hold strategy and 45.17% 20

22 for the automated trading strategy. Clearly, the automated trader experienced higher ROR over a four year period as opposed to the current period beginning in January of b. Stock that is Trading Profitably - CMSB CMSB On August 9, 2011, an open short position was executed. It was purchased for a total value of $ The very next day, the position was closed out. The value of the contract on this date was $ Since this was a short sale, profit is realized when price declines. Thus, the profit from this trade was $ The second trade executed by the Automated Trader was executed on August 10, A long position was executed for a total value of $ This position was held for 13 days, and on August 23 the position was closed. The value on this day was $1,044. Since it was a long position, profit is realized when price appreciates. Thus, the profit from this trade was $

23 On March 4, 2013 a buy position was opened for a cost of $ This position was closed the same day. Since the value decreased to $972.36, a loss was incurred. A loss of $26.64 resulted from this position. The same day, another buy position was opened for a cost of $ This position was held for four days until it was closed on the 8 th of March. The value appreciated to $1,026 and was closed. Thus, a $27.36 gain was incurred on this trade. On March 11, 2013, a buy position was opened at a total price of $ This position was held until November 1, At this date, the price decreased and was worth , which resulted in a loss of $ CMSB After Transaction ROR: Buy-Hold vs. Trading 22

24 In regards to the Buy-Hold Strategy, the ROR during the past 16 trading days has been -0.69%. However, the ROR is higher when a longer period of time is taken into account. The ROR for the current year was 0.90% and 23.15% since June of In regards to Automated Trading, the past 16 days has shown a ROR of 0.62%. However, the ROR since January of the current year has shown a -6.40% decrease but a 45.17% ROR over 1170 trading period (since June 2009). c. Stock that is Not Trading Profitably - DHI DHI On June 1, 2009, an open short position of $ was executed at 9:40 a.m. The very same day the position was closed out two hours later at 11:40 a.m. as the contract value increased to $1,014. Since this was a short sale a loss of $18.36 was incurred as the stock was expected to decrease, rather than increase. The same day, at 12:00 a.m. an open buy position occurred at $ The position was closed out at a valuation of $ at 3:20 p.m. Since it was a buy position, a loss of $20.14 incurred when the value depreciated. On November 12, 2013 a buy position of $ was opened at 11:06 a.m. This position was closed out at 2:06 p.m. with a valuation of $1,003, thus causing a gain of $4.32. The same day, another buy position was opened. At 2:27 p.m. the position had a valuation of The 23

25 position was held for two days then closed out on November 14, 2013 at 10:46 a.m. with a valuation of $1,020. The profit incurred was $ At 12:27 p.m. on November 14, there was another open buy position. The position had a valuation of $ After holding the position for four days, the position was closed out at a valuation of $ on November 18, This devaluation in value caused a loss of $24.50 DHI After Transaction ROR: Buy-Hold vs. Trading In regards to the Buy-Hold Strategy, the ROR was -5.72% since January of the current year. Since June of 2009, the ROR was %. In regards to the Automated Trading Strategy, the ROR during the past 227 trading days was %. However, the ROR was 70.02% since June of Both strategies have shown that current year ROR has been negative, but long term has shown very high returns. It may be concluded that longer periods of time result in a higher ROR. 24