Derivative Valuation, Risk Management, Volatility Trading
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In the previous installment, we discussed the use of a popular asset allocation/market timing rule (10M SMA rule hereafter) to size a short option position. The strategy did not work well as it was the case in traditional asset allocation. We thought that the poor performance was due to the fact that the 10M SMA rule is more of a market direction indicator that is not directly related to the PnL driver of a delta hedged position. Recall that an option position can be loosely divided into 2 categories: dynamic and static [1] 1-Dynamic: the option position is delta hedged dynamically; its PnL driver is the implied/realized volatility dynamics. The profit and loss at the option expiration depends on the volatility dynamics, but not on the terminal value of the spot price. 2-Static: the option position is left unhedged; the payoff of the strategy depends on the spot price at option expiration but not on the volatility dynamics, i.e. it’s path independent. In this post, we will apply the 10M SMA rule to a static, unhedged position. All other parameters and rules are the same as in our previous post. Briefly, the trading rules are as follows 1-NoTiming: Sell 1-Month at-the-money (ATM) put option, no rehedge. 2-10M-SMA: we only sell an ATM put option if the closing price of the underlying is greater than its 10M SMA. Our rationale for investigating this case is that because the payoff of a static, unhedged position depends largely on the direction of the market, the 10M SMA timing rule will have a higher chance of success. Table below summarizes and compares results of the short put strategy with and without the application of the 10M SMA rule
Graph below shows the equity curves of the 2 strategies
As we can see from the Table and Graph, the 10M SMA rule performed better in this case. Although the win percentage and average PnL per trade remained approximately the same, the risks have been reduced significantly. The largest loss was reduced from $2.7K to $1.6K; drawdown decreased from $5K to $1.9K. As a result, the profit factor increased from 1.47 to 1.54. In conclusion, the 10M SMA rule performs well in the case of a static, unhedged short put position. Using this rule, the risk-adjusted return of the trade was enhanced significantly.
Other related studies:
References [1] N.N. Taleb, Dynamic Hedging: Managing Vanilla and Exotic Options, Wiley, 1997 [2] E. Sinclair, Volatility Trading, Wiley, 2nd edition, 2013 Source Here: Using a Market Timing Rule to Size an Option Position, A Static Case
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Last week, Bloomberg reported that due to the low oil price, some producers refused to lock in a loss, and thus stopped hedging.
Oil producers have scaled back locking in future prices “considerably” since February, Societe Generale SA said in a report, citing a shift in options pricing driven by consumer companies like shippers and airlines. Late last year, sellers including U.S. shale drillers locked in prices in droves when benchmarks rose after OPEC announced plans to cut production. “This is a significant shift in the relative producer-consumer hedging behavior,” wrote David Schenck, a cross-commodity strategist at Societe Generale. “While consumers may try to lock in low prices, most producers will simply refuse to lock-in loss-making prices.” Brent’s 12-month put skew closed at its lowest level since May 2016 on Monday. This indicator tends to rise when producers of oil are locking in their supply and fall when consumers, including shippers and airlines, hedge their output. The second-month equivalent was at its lowest level since December 2015. WTI skews have also fallen sharply since OPEC’s last meeting on May 25. Crude in New York touched $42.75 a barrel on Tuesday, the lowest level since Nov. 14, and was closing in on a bear market. Read more 
On the other hand, we recall that Mexico just started its famous oil hedging program by buying put options Mexico has taken the first step in its annual oil hedging program, asking Wall Street banks for price quotes on the put options it buys to lock in prices for the following year, according to people familiar with the matter. The put options give Mexico the right, but not the obligation, to sell oil at a predetermined price and time. The hedge runs from December to November. Read more So who’s right? We note that the Mexican hedgers have had a good track record The Latin American country has received handsome payouts from its oil hedging program, earning a record $6.4 billion in 2015 after OPEC embarked on a war for market share that sent prices tumbling. Mexico made $5 billion in 2009, after the global financial crisis, and another $2.7 billion in 2016. Since the modern oil hedge program started in 2001, Mexico has made a profit of $2.4 billion — its hedges raked in $14.1 billion in gains and paid out $11.7 billion in fees to banks and brokers. The country also made money in the 1990s, when the hedge wasn’t done on an annual basis. ByMarketNews via Derivative Valuation, Risk Management, Volatility Trading http://harbourfronttechnologies.blogspot.com/2017/06/oil-producers-stop-hedging-whos-right.html In the continuation of the “Low Volatility is Not a New Normal” theme, Adam Samson of Financial Times published another post based on the recent report by JPMorgam which suggested using VIX options for managing the risks. Risk assets, like stocks, have been rallying “for years”, sending market volatility near “record lows... While fundamentally volatility should not be high, it is clear to us that the current macro environment does not warrant all-time low volatility either. [caption id="attachment_361" align="aligncenter" width="551"] The article concluded with a suggestion made by the JPM strategist. For US equities, Mr Kolanovic suggests buying out-of-the-money call options on the Vix. The derivatives that are currently “close to their cheapest level over the last five years” would gain in value if the Vix rose over a pre-determined period and pay-out if the index hits a certain “strike” price. The same strategy can be used for the VSTOXX index, which provides a similar measure of implied volatility for the Euro Stoxx 50 that tracks eurozone blue chips. Read more We believe that this suggestion is sound. However, it’s important to note that
These questions should be addressed if we want to increase the efficiency of our hedging or trading strategy. Post Source Here: VIX Options: Should We Buy Them When Volatility is Low? So much is being written about the emergence of “Quantitative Funds” and why this type of investment is becoming popular among both individual and professional investors. Eleanor Laise, in her Wall Street Journal article titled “Stock-Picker Jobs Going to Computers” wrote that “investors are attracted to quant funds for their non-emotional, disciplined method of investing. It is a well known fact amongst investment professionals that “investor psychology” is the most difficult variable for anyone to manage. Our fear and greed most often get in the way of good judgment and a well thought out investment strategy.” One method of developing a quantitative portfolio includes adding alpha to the investment screening process. Although the idea of alpha is thought to be complicated and only for the technically inclined, it’s available for any investor and now easier than ever to utilize. With this strategy readily accessible, it makes sense to build a portfolio of long-term investments and then augment the return by actively trading a portion of the portfolio using technical analysis and portfolio management.
The real question is not if it can be done, but how can it done. Specifically, how does an investor, be it individual or professional, utilize the power of portable alpha? Before the “how to” can be understood, one must appreciate what alpha is and what investments are available that make utilizing portable alpha easy. What is Portable Alpha? According to Lawrence C. Strauss, in his Barron’s Online article titled “Does Low Volatility Mean Lower Returns” alpha “the money-management industry’s buzzword du jour refers to the measure of a stock’s performance beyond what the market provides. But how to calculate Alpha and more importantly how to compare various investment alternatives simultaneously using the same definition of Alpha has been a difficult problem for investors to solve.” Alpha, in its purest sense, is the measure of a fund or portfolio's risk-adjusted return relative to the market. A positive alpha value, such as 1.0, means that the fund or portfolio outperformed the market by 1.0%. The higher the alpha value, the more incremental gain is awarded for actively managing the investment by choosing securities that outperform the market, as compared to merely accepting the market return. Portable alpha is “portable” because it can be applied across various asset classes. If a manager or individual investor increases a portfolio’s risk-adjusted return relative to the market (alpha) by investing in securities that have little or no correlation with the market, then that manager has created portable alpha. Portable alpha is a powerful investment tool because it can provide investors with greater diversification in their portfolios, lower risks and greater total returns as compared to conventional asset allocation. There are other varieties of alpha, but in all cases a positive alpha value indicates that the fund or portfolio manager has "beaten the market" through fund or stock selection. Alpha Advisor Service, LLC uses a weighted alpha factor which places more emphasis on recent price movement as opposed to past activity. The purpose of doing so is to pinpoint stocks and funds whose positive momentum is building rather than those that have reached the peak of their uptrend. Investments That Facilitate Using Portable Alpha Applying portable alpha to your portfolio can be accomplished by using trade-friendly investment funds provided by ProFunds, Rydex or Fidelity. These companies provide a wide variety of mutual fund selections, including index, sector, bond, precious metals, and international, which can be traded frequently, most without penalty, early trading fee or commission. Some of these companies offer funds designed for hedging strategies. Or for the slightly more aggressive, a few of these companies provide leveraged funds which are designed to outperform their benchmark index through the use of leverage. Exchange Traded Funds, which come in as many styles as mutual funds, also provide an easily-accessible tool for adding alpha to a portfolio. Many analytical sources provide statistical profiles of investments, most of which are mathematically accurate. The predominant short coming in these tools is that they do not consistently analyze all alternatives. Bond investments will be measured using benchmarks unique to bonds while small cap stocks will be measured against the Russell 2000 etc. To select the best investments, using a level playing field by which to measure portfolio returns is the most attractive. How to Utilize Portable Alpha The first step towards utilizing portable alpha involves developing an asset allocation strategy specifically tailored to personal investment objective, risk tolerance and time horizon. Determine how much of the portfolio should be strategically allocated to specific asset classes such as stocks, bonds, sectors, international investments, precious metals and cash. Assign a percentage of investment dollars to each class, and then prepare to fill in the asset class with an appropriate selection of investments. To select the best investments for each asset class, rank the investments by alpha score from highest to lowest. Then pick the top one or two options for investment within each asset class. Put in place a trailing stop loss on each investment at a reasonable level and watch its performance. If the price violates your watch level, sell the investment and replace it with the next most highly ranked alternative from its class. If no alternatives are available with a positive alpha, hold those dollars in cash until such time as a candidate presents itself. Don’t invest those dollars in another asset class; hold them until a candidate in the particular class becomes available. This approach satisfies the buy and hold dogma that is unfortunately so engrained in the minds of today’s investors. It supplies adequate diversification while at the same time providing a level of return that’s in line with market expectations. Hopefully, by this point recent market activity has convinced most investors that the idea of buying a stock or fund and holding it indefinitely is no longer the optimal investment strategy. Human nature has a tendency to result in buying and selling at the worst possible moments, minimizing gains and maximizing losses. That’s why the development and implementation of a disciplined investment strategy is so advantageous to today’s investors. Taking this approach one step further and evolving from a strategic allocation to a tactical or dynamic allocation is the easiest way to generate excess investment returns within a buy and hold strategy. Tactical allocation is predicated on the belief that not all asset classes perform in the same manner and that investment cycles do exist. With so many index funds and ETF’s that mimic the performance of market indices and style-box investments, analyzing the alpha scores of these investments is the quickest way to determine where to increase or decrease a portfolio’s allocations. Today, with so many internet-based trading platforms available through brokerage firms and banks with minimum fees and almost no trading commissions, active personal investing makes more sense then ever. Affordable high-speed internet connectivity, computers, cell phones and internet brokerage accounts coupled with powerful mathematical statistics such as portable alpha are negating any excuses for experiencing unacceptable investment returns. A convertible bond (or preferred share) is a hybrid security, part debt and part equity. Its valuation is derived from both the level of interest rates and the price of the underlying equity. Several modeling approaches are available to value these complex hybrid securities such as Binomial Tree, Partial Differential Equation and Monte Carlo simulation. One of the earliest pricing convertible bond approaches was the Binomial Tree model originally developed by Goldman Sachs [1,2] and this model allows for an efficient implementation with high accuracy. The Binomial Tree model is flexible enough to support the implementation of bespoke exotic features such as redemption and conversion by the issuer, lockout periods, conversion and retraction by the share owner etc.
In this post, we will summarize the key steps in pricing convertible bond method using the Binomial Tree approach. Detailed description of the method and examples are provided in references [1,2]. Generally, the value of a convertible bond with embedded features depends on:
where S0 is the stock price at the valuation date; u and d are the up and down jump magnitudes. The superscript j refers to the time step and i to the jump. The up and down moves are calculated as and where is the stock volatility, and is the time step. The risk neutral probability of the up move, u, is and the probability the down move is 1-p After building a binomial tree for the common stock price, the convertible bond price is then determined by starting at the end of the stock price tree where the payoff is known with certainty and going backward until the time zero (valuation date). At each node, Pj,i the value of the convertible is where m denotes the conversion ratio. If the bond is callable, the payoff at each node is The payoff of a putable bond is Here C and P are the call and put values respectively; r denotes the risk-free rate. The above equations are the key algorithms in the binomial tree approach. However, there are several considerations that should be addressed due to the complexities of the derivative features
References [1] Valuing Convertible Bonds as Derivatives, Quantitative Strategies Research Notes, Goldman Sachs, November 1994. [2] Pricing Convertible Bonds, Kevin B. Connolly, Wiley, 1998. The process of investing is a great way for you to earn potential income. Hardly any people have the knowledge to be able to suceed, however, so many people rely upon brokerages to manage their portfolio for them. There are, however, some common investing mistakes that people make that can result in huge losses and missed opportunities. Here are a list of the absolute worst mistakes to avoid when investing in the stock market.
Mistake #1 - Invest When Youre Old You are never too young to start investing in the stock market - in fact, it's recommended to get started sooner. The perception of investing is that it is reserved for older, financially established people who can invest large sums of money. This is a misconception that is limiting people from tapping into the power of investing. Waiting just ten years can make a huge difference in the total gains that one can make over their lifetime. For example, investing just $2000 a year (thats just $170 a month) starting at the age of 26 can yield $2,114,379 by the time you are 75. This is with an Annual Return Rate (ARR) of 10% per year steady through the life of the investment. The same investment, with the same ARR, made ten years later at the age of 36 will result in a return of only $802,895 at the age of 75. That is a 1. 3 million dollar difference. If you are not able to invest as much as $160 a month, set aside $25 per month. Even this small amount can have a large impact over time. Mistake #2 - Not Understanding The Company It is shocking that many people will put more time and research into choosing an MP3 player or home theater system than they will researching the stocks they will invest in. It is imperative that you take the time to understand the financial history of the companies you wish to have shares with. Make sure that you understand what you are buying and how it will benefit you in the long run. It is also important to keep in mind that you must remain objective when choosing stocks. Stocks that you have researched well and carefully selected are more likely to increase than ones you choose based on a œfeeling. Put your emotions aside and consider your options carefully. Taking time to research and investigate is also important when choosing your financial advisor. Consider meeting with a few candidates and evaluating their approach to investing. If you are meeting with someone on a recommendation, make sure that the person who recommended the advisor is someone who is qualified to do so. Mistake #3 - Gambling On Stocks Another common mistake is confusing gambling or speculating with investing. Investing in stocks is part of a long- range financial picture and not a get- rich- quick scheme. While there certainly are high yield quick return programs out there, it is wise to limit your participation in those programs. Day trading is one of these types of programs. When someone is involved in day trading they trade very rapidly in and out of stocks in order to profit daily from marginal changes in the market. This practice may seem easy to profit from but it actually results in more losses for investors than gains. Similarly, some try investing over a short period of time in very risky stocks. A short- term investment of six months to a year in a œhot stock does not belong in a well- thought out financial plan. True investing should be done in quality companies over a period of several years. Finally, listening to someone who has a œhot tip is a quick way to lose a lot of your investment. Research any tips you get carefully and only invest if the numbers pan out, no matter how much others insist that this is the stock to have. Mistake #4 - Putting All Your Eggs In One Basket Don't underestimate this old addage. In any portfolio, you will want to diversify your holdings. Additionally, having too much stock in one specific industry can also be a recipe for disaster when the market changes. Spread your money over several different companies and different industries. That way there would have to be some catastropic disaster in order for you to lose all your money. |
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VVIX as at June 23, 2017. Source: Interactivebrokers[/caption]
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