Showing posts with label baseline-risk-assessment-mining. Show all posts
Showing posts with label baseline-risk-assessment-mining. Show all posts

RISK, REWARD, AND SAFETY- Baseline Analysis

RISK, REWARD, AND SAFETY


Baseline Analysis

Reaction and Challenge

Many of them were horrified to hear that I was dealing with uncovered puts. "Too risky," they said; "It's doomed to failure;" ''The gains you make on successful deals will be overwhelmed by gigantic losses on your losers." Listening to them would have you convinced I was playing the ponies or gambling in Las Vegas. It's not hard to understand these initial reactions; after all, Characteristics and Risks of Standard Options, a joint publication of the various option exchanges, emphatically states that "as with writing uncovered calls, the risk of writing put options is substantial." This warning is repeated in the companion pamphlet Understanding Stock Options. 

Few seemed to recall the statement made in the former publication: ''The risk of being an option writer may be reduced by the purchase of other options on the same underlying interest—and thereby assuming a spread position—or by acquiring other types of hedging positions in the options markets or other markets." How could I convince other investors  that what I was doing had the potential to increase the rate of return on my investment portfolio without unnecessary risk? After all, people do invest their funds in uninsured money market funds paying 5 percent a year rather than federally insured passbook savings accounts paying just 3 percent a year. The added return must bring with it a certain degree of added risk, yet almost everyone is willing to accept the risk/ reward ratio in this situation.

Methodology

To address this issue, imagine what would have been the outcome if each month over some extended period, one sold an at-the-money (ATM) LEAP put on every company for which LEAPS existed and pocketed the premium. The period selected was the ten year period ending March 31, 1997. This cutoff date was selected because on that date the Dow Jones Industrial Average stood at 6,583 and the Nasdaq composite index was at 1,222, both well below their closing values for 1996 and close to their lows of 1997. In that manner, the phenomenal run-up that has taken place in the stock market since then was effectively eliminated.

Because of mergers, acquisitions, and spin-offs, about three dozen of these companies are no longer independent entities and/or have changed their names since then. These include Air Touch, Amoco, Bay Networks, Borland, Chrysler, Citicorp, Columbia Gas, CUC International, Digital Equipment, DSC Communications, Dun & Bradstreet, ENSEARCH, First Chicago, General Instrument, HFS, ITT, Marriott International, Mobile Telecommunications, NationsBank, NYNEX, Pacific Telesis, PHP Healthcare, RJR Holdings, Salomon, Signet Bank, SunAmerica, Tambrands, TCI, Telephonos de Brasileras, Travelers, U.S. Robotics, U.S. Surgical, Westinghouse, WMX Technologies, and Woolworth.

By the time you read this, other reorganizations will have undoubtedly taken place. Of course, LEAP puts did not come into being until 1990, and even then they only appeared on just a handful of stocks, so you will have to imagine for the moment that such puts had been in existence for those 217 equities over the ten-year period ending on March 31, 1997. Because LEAPS did not exist for most of these issues over that period, no historical information is available on the premiums that such options would have commanded. What was done instead was to use the daily history of closing stock prices over that decade to compute historical volatility, and from this to use the standard BlackScholes formula for computing the LEAP put premium on a month-to-month basis. 

So as not to make the modeling process too complex, the risk-free rate of return was kept at 6 percent per year throughout, and all volatility calculations were based on the prior one-year price history. In each instance, the at-the-money put selected was the one for which the strike price was equal to or immediately below the market price of the underlying issue in accordance with standard option rules: If the price of the stock was $23, the option sold was the one at $22.50; if the price was $44, the option sold was the one at $40; and if the price was $247, the option sold was the one at $240. In most instances, there would have been not just one but two such LEAP puts available for sale each month: the one that expired in the January about a year to a year and a half away, and the one that expired in the January about two to two and a half years away. 

We will call these the near and far LEAPS, for the lack of better terms. If the expiration date of the near LEAP put was less than eight months away, it was not sold, as we want to restrict the study to an analysis of long-term options. A database containing the ten-year history of daily high, low, and closing prices of the 217 common stocks that had LEAPS on March 31, 1997, was downloaded from the America Online historical price files. Also shown are the volatilities calculated for March 31, 1997. The figures range from a low of 0.150 for Amoco Corporation to an unusually high 1.456 for Compania Tele de Chile. Only 10 of the 217 stocks had volatilities greater than 0.65. The First Call rating system generates a numerical average determined from the ratings supplied by the industry analysts who follow the stock. An individual analyst's ratings range from 1 (strongest recommendation) to 5 (strong sell). 

Because of the averaging technique involved, it is rare to see First Call ratings worse than 3.5. The S&P ratings range from A+ (strongest possible) downward. Just one stock (Pitney Bowes) was not rated by First Call, while 37 stocks were not rated by Standard & Poor's. Most of the issues not rated by S&P represented American Depositary Receipts (ADRs) of foreign stocks. For the 216 issues with First Call ratings, the average is 2.1, which is slightly better than the average rating of about 2.2 for the universe of stocks rated by First Call. Among the 180 issues with S&P ratings, the average is just under B+. (The S&P average was calculated by letting A+ = 5.0, A = 4.5, A- = 4.0, B+ = 3.5, B = 3.0, B- = 2.5, C+ = 2.0, and C = 1.5. The numerical average calculated on this basis was 3.4.)

The Simulation Model

After downloading the historical data, I constructed a detailed simulation model that could calculate the effects on each of the 217 issues of having sold a put each month for the period from January 1987 (or whenever the company came into being) through March 31, 1997. The two extra months (January and February) in 1987 were included to allow more accurate computation of initial volatilities. More important was the fact that I started the analysis with 1987 because I wanted to include one of the worst days ever from the viewpoint of put sellers—the market decline of 22.6 percent on October 19, 1987.

Each data history file contained the daily high, low, and closing prices for the stock from January 1, 1987, onward. It is possible to distort the results if the LEAP puts are consistently taken as being sold at that point each month when the underlying issue achieved its low price (and hence commanded its highest put premium). So as not to bias the results, the assumption was made that all LEAP puts were sold at the closing price on the last day of the month. It is also possible to distort the results if the LEAP puts are consistently taken as being sold only in the month or months when the underlying issue achieved its low price

It was for this reason that the assumption was made that LEAP puts were sold on each stock each and every month during the calendar year. Another way to distort the results is to select a cutoff date ending on a sharp upbeat in market prices. As mentioned earlier, it was to minimize this possibility that the cutoff date of March 31, 1997 (close to the low of the year), was selected for the financial simulation rather than some later point in time during the market's rapid ascent to current levels. Finally, there is the selection of the option-pricing formula. To adopt as conservative an approach as possible, all premiums were calculated by ignoring dividends and early exercise (i.e., European-style options).

Table  LEAPS Available in March 1997

 

Table  LEAPS Available in March 1997 (Continued)



Table  LEAPS Available in March 1997 (Continued)



Table  LEAPS Available in March 1997 (Continued)


Table  LEAPS Available in March 1997 (Continued)


Adopting these procedures I have outlined effectively eliminated any attempt to maximum LEAP premiums by timing the market or influence the results by selecting a good year to start or a market peak at which to evaluate the final outcomes. All other baseline assumptions and specific output results are summarized in the sequence of tables that follow.

The Results

The number of near-term puts sold is less than the number of far-term puts because of the minimum eight-month expiration period that was imposed on the process. Of the 21,976 near-term puts sold, 20,022 of them would have reached their expiration dates prior to the end of the simulation on March 31, 1997. Of the 23,914 far-term puts sold, 19,383 of them would have reached their expiration dates. The remaining 1,954 near-term active LEAP puts and 4,531 far-term active LEAP puts represent open interest and are investigated as well.

Of the 20,022 near-term LEAP puts that expired, 15,178, or 75.8 percent, expired out-of-the money (OTM), with no financial exposure to the put writer.* This left 4,844, or 24.2 percent, of the near-term LEAP puts to expire in the money (ITM). In a similar manner, of the 19,383 far-term LEAP puts that expired, 15,457, or 79.7 percent, expired out of the money, and 3,926, or 20.3 percent, expired in the money. The percentage of the far term puts that expired in the money is thus smaller than that of the near-term puts (20.3 percent versus 24.2 percent). This is a result of the additional year that the underlying stock had to recover from any financial difficulties encountered along the way, as well as of the natural growth of earnings during that time frame.

The premiums collected were $3.8 million on the near-term LEAP puts and $4.5 million on the far-term LEAP puts. The total of almost $8.4 million in premiums shown is just for the 39,405 LEAP puts that expired, not for the total number of 45,890 written. So as to establish a baseline of the premiums received and financial exposure encountered, no hedging strategies whatsoever were adopted on this initial run. The premiums received in this baseline run were presumed to be immediately invested in money market funds earning a risk-free rate of return of 6 percent. Such funds, if left on deposit and compounded to the end of the simulation run on March 31, 1997, would be substantial. 

To focus on the underlying mechanics of the overall process. The combined total amount of the LEAP premium and the interest earned through expiration is called the forward value of the premium, and is seen to be $4.1 million for the near-term LEAPS and $5.1 million for the far-term LEAP puts. It is the forward value of the premiums that is then used to cover the financial exposure incurred by various LEAP puts that expired in the money. Financial exposure is the difference between the stock price and the strike price at expiration, if the latter is greater. For the 4,844 near-term LEAP puts expiring in the money, the financial exposure is $2.7 million, which is equivalent to an average potential loss of $558 per contract. 

For the 3,926 far-term LEAP puts expiring in the money, it is $2.9 million for an average potential loss of $743 per contract. Why is the average loss on the far-term ITM LEAP puts greater than the average loss on the near-term ITM LEAP puts? The reason is that the universe of 217 stocks includes several lower-rated issues that fared very poorly over the ten-year period investigated. Because of the virtually downhill price histories of these particular issues, the longer the term of the LEAP put, the greater the financial exposure encountered. On the other hand, the higher premium associated with far-term LEAP puts often more than offsets the higher level of financial risk involved. 

To see this, note that the realized gain on the near-term LEAP puts is calculated as the $4,081,004 forward value of the premiums less the $2,701,176 in financial exposure involved, or $1,379,828. This realized gain as a percentage of the $3,828,194 in premiums collected on the near-term LEAP puts is 36 percent, and is referred to as the retention rate. For the farterm LEAP puts, the retention rate is 48.1 percent. So while the average loss on the farterm ITM LEAP puts is higher, so is their retention rate. The overall retention rate is 42.6 percent. The premiums collected on the 1,954 active near-term LEAP puts totaled $698,972. 

When invested at 6 percent per year (compounded monthly), they were worth $712,791 on March 31, 1997. These active near-term LEAP puts had a residual value of $652,565 on that date, for an unrealized gain of $60,226. In a similar manner, the unrealized gain on the 4,531 active far-term LEAP puts was $266,175. The total unrealized gain was thus $326,401 on March 31, 1997. The number of active far-term LEAP puts is going to be much larger than the number of near-term LEAP puts because there are that many more of them whose expiration date is later than March 31, 1997.

Shows the effect of leaving the net realized gains on deposit to compound at 6 percent interest from expiration through the end of the study period on March 31, 1997. A total of $10,836,330 in premiums would have been received over the ten-year study period on the 45,890 LEAP puts written, including both expired and still-active LEAP puts. By March 31, 1997, the total realized gain and interest earned from the sale of the expired LEAP puts would have been $4,471,186. Combining this with the unrealized gain of $326,401 on the active puts yields an overall account value on March 31, 1997 of $4,797,587.

As a final, we note that the account value of close to $4.8 million on March 31, 1997, is 44.3 percent of the $10,836,330 in premiums generated over the course of the run. It is to be emphasized that it is not the account value of $4.8 million nor the $10.8 million in premiums that is important here but rather the ratio of the two. Obviously, no one is going to sell one or more LEAP puts each month on every one of the possible stocks for which LEAPS are available. What we have established is that if you had sold a random number of at-the-money LEAP puts on a random number of stocks on a random schedule throughout each year over the past ten years, and invested the net premiums in money market funds, the expected value of your account balance at the end would be about 44 percent of the total premiums ever collected.

The realized and unrealized gains determined here ignore the effect of taxation and all transaction costs, fees, and commissions. These can be significant because irrespective of the holding period involved, the gains on puts that expire worthless are treated as short-term capital gains. On this basis, after-tax results on a net commission basis would be somewhat smaller than those shown in the tables. Of course, this isn't the real problem associated with the above results. The real problem is the high level of financial exposure relative to the premiums collected. 

Although only 22.3 percent of the LEAP puts will expire in the money, their effect is to force the return of 58.4 percent of the forward values of the premiums receivedIn view of this, maybe my friends were correct in saying that ''the gains you make on successful deals will be overwhelmed by gigantic losses on your losers.'' On the other hand, surely one could decrease one's financial exposure by being more discriminating about what stocks to select for selling LEAP puts on, as well as by adopting appropriate hedging strategies, such as the use of spreads and rollouts and the selling of out-of-the money puts. Each of these techniques will be considered in the chapters that follow.

RUN NUMBER 1

ATM Strike Price Is the High, Low, or Closing Stock Price:                        C
No. of Steps LEAP Put Is below the ATM Strike Price:                                 0
Minimum No. of Months till Expiration:                                                         8
Premium Reinvestment Rate:                                                                            6.0%
Minimum First Call Rating:                                                                                5.0
Minimum Standard & Poor's Rating:                                                               None
No. of Stocks Meeting Either Criterion:                                                           217

Table  LEAP OTM and ITM Rates

Table  Premiums Collected and Realized Gain for Expired LEAPS


Table  Premiums Collected and Unrealized Gain on Active LEAPS


Table  Premiums Collected and Account Values



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