Hedging Equity - Case Study Example

Hedging Equity Prices for indices and futures The prices for indices and futures are as shown in the figure below as of 19th June,2015. Figure1: prices for indices and futures (Barchart.com Inc. 2015) Advantages and disadvantages of using options to hedge It is flexibility in that the user of options enables a trader to trade any potential move as far as the underlying security is concerned. In this case, the investor can use them even to protect his downside. Options also enable one to employ considerable leverage. The trader can gain incredible leverage as well as returns of 100% or higher. Another advantage is the directional choice that is related to flexibility as the trader can use them to trade downward and upward and even sideways price movements (LearnMoney.co.uk 2015). Through the use of options strategies, the trader can reduce risks as they can allow similar leverage profit potential. Another advantage of using options is its ability to allow the trader to sell them against shares that he or she already owns. Through this option, the trader can earn extra income from the sale of these shares. On the other hand, option strategies have some drawbacks. Options can be of high risk even though they are designed to reduce risks. Options fall the risk-reward ration in that, options with higher returns are also characterized with greater risks and vice versa. Also, even though options have got the leverage advantage, it also has disadvantages arising from the leverage as the loss resulting from them can be horrible since all losses are multiplied. This is especially where too much leverage is used. The use options are also sophisticated in that it takes long for someone to know how it works (LearnMoney.co.uk 2015). Options are also risky where there is less information about the quotes as well as other analytical information such as the implied volatility. Dunbar (2012) notes that, options are also not available to cover all stocks as it limits the number of possibilities available to the trader. Another limitation of using the options strategies is the highest commission per dollar invested, which is incurred during their trade. This is especially common for spreads where an investor pays commissions for both spread sides. According to the ThinkTrade.net (2006), the options have higher spreads due to the lack of liquidity. This makes the trader incur more costs in the form of indirect costs when trading them as he will be giving up the spread. There is always a waste of assets since options lose value over time. Therefore, the traders should be right on the direction as well as his timing. Zero cost collar According to Arunajith (2007), the zero cost collars are also called the castles collar and is an option trading strategy, whose use is in the short term so as to seek protection from short-term volatility of market forecasts. This is one of the two collars that are mostly used by investors. It is the best strategy for bullish investors who believe that the underlying will continue gaining value. This type of a collar entails the purchase of a put as well as the sale of a call, where the strike price of a call is set to generate enough cash to pay for the put (Gilmour 2014). Through the use of the zero cost collars, an investor can costlessly hedge while still retaining potential for profit in the position (Gordon 2015). According to Marie (2012: 113), the zero cost collar combines put spreads with short calls, thereby lowering the risk by half as it also helps in preserving long-term returns. One of the strategies that an investor uses to hedge against the risk of a price drop of the involved asset is the Inverse Vertical Ratio Put Spread Strategy. Other techniques are the Short Put Ladder Strategy and the Short Call Ladder Strategy. Arunajith (2007) notes that the zero cost collar is used to create a position of a synthetic future. Black-Scholes Option Pricing Model This is a technique used in the determination of the value of options (Kaplan Financial Limited 2012). Hoadley (2015) notes that this model is used in the calculation of the theoretical call price using the five core determinants of the price of an option and which include: price of the stock, strike price, short-term (risk free) interest rate, volatility and time to expiration. While using the Black-Scholes Model to value options it is assumed that, over the options life, the risk-free rate does not change, and the volatility of the stock price, as measured by the stock’s standard deviation does not also change over this life of the option. This Model is also used to predict the unknown variable of the option if they market price of such an option is given. Additionally, this Model is used to estimate the implied volatility that is utilized in the markets pricing of options by computing the standard deviation. Limitations of the Black-Scholes Model According to Ray (2012: 175), even though the Black-Scholes Model is popular and widespread used, it suffers some loopholes because it has been built on some non-real life assumptions especially, in relation to the market. The mathematical skills required in the derivation as well as its solution are some problems facing most of the economics as it could probably be unfamiliar to them. This paper thus identified several shortcomings of the Black-Scholes Model. First, limitation lies with its assumption that stocks move in a random walk. In this case, the random walk implies that at any particular moment, the underlying stock’s price can rise or drop with the same probability. Ray (2012) argues that this assumption is invalid since there are many factors determining prices of stocks, and which cannot be assigned the same probability in their likely effects on the stock prices. Secondly, even though the volatility can be comparatively constant, it is only possible over a very short term and never in the long term (Dunbar 2012). In simple terms, it has been found that for financial time series, and after the consideration of logs as well as first differences, the volatility level appears to change with time. Often, high volatility periods follow immediately after a significant variation, often downward, in the original series level and it may take rather some period for this heightened volatility to subside. Substantial price variations are followed by significant price changes, and contrariwise leading to volatility clustering. It should be noted that volatility measures are negatively correlated with the returns of assets while the trading volume is positively correlated. Therefore, the volatility fails to be constant. The third drawback of the Black-Scholes Model is its assumption that the log returns have a normal distribution underlying the prices of stocks is rational in the actual world (Rubash 2015). The assets’ returns have a finite variance as well as semi-heavy tails opposite of the stable distributions like log normal, which is characterized by infinite variance as well as heavy tails. The fourth shortcoming is on the Black-Scholes Model’s assumption that there are no dividend distributions by the underlying stock during the duration that the option is held. This is a limitation since such a case does not happen as the majority of the publicly traded companies pay some dividends to their shareholders (Ray 2012: 175). The fifth limitation is based on the assumption that there are no fees during the sale and purchase of stocks and options and no barriers to trade (Rubash 2015). This does not hold as stock brokers earn their fee by charging some rates based on some criteria such as spreads. Another connected limitation is the assumptions that markets are perfectly liquid, thus facilitating the buying or disposing of any stock or options amount at any given time. The sixth shortcoming of the Black-Scholes Model is in its assumption that the interest rate is known and constant. This is unrealistic as in the real world as risk free situations do not exist, other than in cases of government treasury bills, and of which their rates still change in times of increased volatility (Rubash 2015). Other considerations Given that the Black-Scholes Model has some shortcomings, it is not a panacea to the option pricing issues. Therefore, it is prudent that some adjustments are made to it so that it can approximate the options prices with minimal drawbacks. In this regard, several parameters need to be established. Among them is the delta, which is a Black-Scholes Model’s by-product. The delta means the degree to which the price of the option moves gives a small variation in the underlying stock price. In the case of deeply out of the money call, its delta nearest zero while deep in the money call has a delta of very close to one (Hoadley 2015). The Delta is the hedge ratio. A position delta also known as the Equivalent Stock Position is established and measures the range of stock prices as well as the days to expiration. Another critical Greek in the construction of option strategies is the gamma. It is computed to measure how fast the delta varies for small variations in the underlying stock price. According to Hoadley (2015), this is the delta of the delta. Whenever a portfolio is hedged using the delta hedge technique, then, the gamma is kept as small as possible with a view to making it easy to reset the hedge with a view to maintaining a delta neutral position. A too large gamma is likely to wreck the hedge. Another important Greek is the Vega, and it is the variation in the price of the option as a result of a 1% change in volatility. Vega is also used for hedging purposes just like the gamma and the delta. Theta is the other Greek, and it is the variation in the price of the option given a one-day drop in the remaining time of its expiration. It is used to measure the time decay. Hoadley (2015) argues that it would be pointless to hedge a portfolio against the time decay because the passage of time is inexorable and constant. Rho is similarly an important Greek that should be considered in the construction of option strategies. It measures the variation in the price of the option given a 1% variation in the risk-free interest rate. References Arunajith, U. (2007, May 13) The zero cost collar hedging strategy. Financial Times, p. http://www.sundaytimes.lk/070513/FinancialTimes/ft315.html. Barchart.com Inc. (2015) Indices Futures Prices. Retrieved June 19, 2015, from http://www.barchart.com/futures/Indices Dunbar, S. R. (2012) Limitations of the Black-Scholes Model. Retrieved June 19, 2015, from http://www.math.unl.edu/~sdunbar1/MathematicalFinance/Lessons/BlackScholes/Limitations/limitations.xml Gilmour, J. (2014) Directors trend of zero cost collar hedging. Retrieved June 19, 2015, from http://www.moneyweb.co.za/archive/directors-trend-of-zero-cost-collar-hedging/ Gordon, R. N. (2015) Hedging Basics - CBOE. Retrieved June 19, 2015, from Chicago Board Options Exchange: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0CDoQFjAE&url=http%3A%2F%2Fwww.cboe.com%2FInstitutional%2Fhedge.pdf&ei=_FqFVbSmPKXa7gbN7IGwDA&usg=AFQjCNF5wcpfdvWR42Mc3HVDSKcnHB2cvg&sig2=o8N3b7mVSaGORYFVbowvLA&bvm=bv.96339 Hoadley, P. (2015) Option Pricing Models and the "Greeks". Retrieved June 19, 2015, from http://www.hoadley.net/options/bs.htm Kaplan Financial Limited. (2012) Black-Scholes option pricing model. Retrieved June 19, 2015, from http://kfknowledgebank.kaplan.co.uk/KFKB/Wiki%20Pages/Black%20Scholes%20option%20pricing%20model.aspx?mode=none LearnMoney.co.uk. (2015) Options: Advantages & Disadvantages. Retrieved June 19, 2015, from http://www.learnmoney.co.uk/options/pros-cons.html Marie, B. (2012) Hedging of Sales by Zero-cost Collar and its Financial Impact. Journal of Competitiveness, 4(2), 111-127. Ray, S. (2012) A Close Look into Black-Scholes Option Pricing Model. Journal of Science (JOS) 172, 2(4), 172-178. Rubash, K. (2015) A Study of Option Pricing Models. Retrieved June 19, 2015, from http://bradley.bradley.edu/~arr/bsm/model.html ThinkTrade.net. (2006). The advantages and disadvantages of options. Retrieved June 19, 2015, from http://www.thinktrade.net/options-advantages-and-disadvantages.php Read More