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How To Tell The Difference Between The Graham Formula And The Graham Number

This article will aim to help you as a reader understand the difference between the Graham Formula and the Graham Number. The Graham Formula is the formula which Benjamin Graham provided in his classic book The Intelligent Investor. The Graham Number is a figure used by some investors as an upper limit to how much an investor should pay for a stock. The Graham Number formula was never actually provided by Benjamin Graham. Even though the Graham Number isn’t used in the ModernGraham approach, the figure is now provided with each individual ModernGraham valuation. (click to enlarge) Often I get questions about the Graham Formula versus the Graham Number. There seems to be some misunderstanding out there between the two concepts, and this article will aim to help you as a reader understand the difference between the Graham Formula and the Graham Number. Both figures can be useful in their own ways, and can be combined in the ModernGraham approach. What is the Graham Formula? The Graham Formula is the formula which Benjamin Graham provided in his classic book The Intelligent Investor . Specifically, the formula Graham recommended is: According to Graham, this formula resulted from a study of various valuation methods and is to be considered an effective shorthand way of estimating the intrinsic value of stocks. The formula should result in figures “fairly close to those resulting from the more refined mathematical calculations.” Where does the Graham Formula Come From? Graham placed the Graham Formula in Chapter 11 of The Intelligent Investor , titled “Security Analysis for the Lay Investor: General Approach.” This chapter deals specifically with finding ways to simplify some of the complex mathematical analysis methods which have grown in popularity over the years. After dealing with analyzing bonds and preferred stocks, Graham addresses the issue of valuing stocks, beginning with the sentence “The ideal form of common-stock analysis leads to a valuation of the issue which can be compared with the current price to determine whether or not the security is an attractive purchase.” Graham then went into some detail regarding how many valuation methods utilize future estimates of various figures such as sales, operating margin, etc. in order to then capitalize those figures back to the present in order to determine a value based on the future earnings of the company. However, he then said that “The reader will note that quite a number of the individual forecasts were wide of the mark.” Further, the present value of future earnings is widely dependent on various factors such as: General Long-Term Prospects. Management. Financial Strength and Capital Structure. Dividend Record. Current Dividend Rate. Discussion of each of those factors is beyond the intended scope of this particular article, but together those items constitute items that an analyst must consider when determining an intrinsic value. With all of that in mind, it makes sense that Graham then proceeded to provide the Graham Formula as a way to simplify some of the process for the lay investor. Analysts can spend a lot of time considering each and every little detail about what they think a company is going to do, generating complex mathematical formulas and scenarios in order to determine a value, but Graham’s formula is intended to help the average Intelligent Investor to estimate a value while making as few assumptions about the company as possible. What about the Footnote? Immediately after listing the formula itself, Graham stated that “The growth figure should be that expected over the next seven to ten years.” He also included a footnote on that sentence. The footnote reads: Note that we do not suggest that this formula gives the “true value” of a growth stock, but only that it approximates the results of the more elaborate calculations in vogue.” Some have taken that footnote to mean that the Graham Formula should not be used for estimating an intrinsic value, but I consider the footnote to be more of a reminder from Graham that the calculation of an intrinsic value is not an exact science and cannot be done with 100% certainty. Rather, the investor can only estimate at the intrinsic value due to the vast number of variables involved. Graham provided this formula specifically as a way to approximate the more complex formulas used in an analysis in order to give a “foreshortened and quite simple formula for the valuation of growth stocks, which is intended to produce figures fairly close to those resulting from the more refined mathematical calculations.” Therefore, the Graham Formula is to be used for estimating intrinsic value within a margin of safety which will accommodate the possibility of error in calculation. What is the Graham Number? The Graham Number is a figure used by some investors as an upper limit to how much an investor should pay for a stock. Here’s an example of how some investors use the Graham Number when analyzing dividend aristocrats. The Graham Number is calculated using this formula: According to the Graham Number calculation, the price must be below the square root of the product of 22.5, the Earnings Per Share, and the Book Value Per Share. Where does the Graham Number Come From? The Graham Number formula was never actually provided by Benjamin Graham. Rather, it seems to be engineered out of one of Graham’s recommended requirements for the Defensive Investor. In Chapter 14 of The Intelligent Investor , Graham provided a list of suggested criteria to help the Defensive Investor find quality securities for consideration. Those criteria are as follows: Adequate Size of the Enterprise A Sufficiently Strong Financial Condition Earnings Stability Dividend Record Earnings Growth Moderate Price / Earnings Ratio Moderate Ratio of Price to Assets In the seventh criteria, Moderate Ratio of Price to Assets, Graham says that “Current prices should not be more than 1.5 times the book value last reported. However, a multiplier of earnings below 15 could justify a correspondingly higher multiple of assets. As a rule of thumb we suggest that the product of the multiplier times the ratio of price to book value should not exceed 22.5.” The 22.5 number comes from the product of his suggested maximum price to earnings ratio of 15 and the suggested maximum book value of 1.5. Somewhere along the line, analysts took this suggestion from Graham and extrapolated it into the Graham Number. The Graham Number is Only a Shorthand Version of the Graham Requirements for Defensive Investors. It is my belief that the Graham Number is only a way to easily and quickly screen companies to be used by individual investors not interested in applying all of Graham’s suggested investment techniques. In some ways it seems to be a figure created to simplify Graham’s work into a single recommendation, which to me seems to miss the overall point Graham is trying to make altogether. The Defensive Investor requirements are intended to assist the investor in narrowing down his potential list of investments to only those that are of the highest quality. Graham provided a list of suggested requirements to achieve that purpose, while he specifically provided the Graham Formula as a metric for estimating the intrinsic value of companies. Why would Graham have listed the suggested criteria in an area separately from the formula if he did not intend both items to be used? What Approach Does ModernGraham Use? Here on ModernGraham, I’ve developed our approach to utilize the full breadth of Graham’s recommendations. This is through utilizing both the suggested selection criteria to narrow down the list of potential investments and through the use of the formula to estimate an intrinsic value. Doing this allows the investor to narrow down the focus to a select number of companies and then generate an estimated intrinsic value based on the Graham Formula for comparison to the current price. Each ModernGraham valuation of a company begins with determining whether it is suitable for either the Defensive Investor or the Enterprising Investor, based on a modernized version of Benjamin Graham’s suggested selection criteria for each investor type. Here’s a great post on how you can determine which type of investor you are. After that step is completed, the valuation continues to determining an estimated intrinsic value for the company based on the ModernGraham formula. The ModernGraham formula has been modified slightly from the Graham Formula, only in the sense that it uses a weighted-average of five years of earnings data (EPSmg). The rationale is that Graham suggested using a normalized earnings per share figure in order to smooth out the effects of the business cycle, and also specifically suggested taking an average of earnings per share data when using the figure in analysis. You can learn more about how to estimate a growth rate in this post. Here’s the ModernGraham Formula: This formula is specifically intended to provide only an estimate of the company’s intrinsic value and must be utilized in tandem with a margin of safety because it does not provide an exact figure but only approximates some of the more complicated valuation methods. ModernGraham utilizes multiple layers of safety margins including: Maximum possible estimated growth rate of 15% Estimated growth rate is reduced by 25% To receive a rating of “undervalued” a company must be trading at 75% or less of its intrinsic value. To receive a rating of “overvalued” a company must be trading at 110% or more of its intrinsic value. Each valuation is intended to be a useful source for investors to utilize when conducting research into investment opportunities, and after the first two steps of the ModernGraham analysis, investors are encouraged to continue their research in order to determine if the opportunity is right for their own individual situation. Where Can You Find the Graham Number? Even though the Graham Number isn’t used in the ModernGraham approach, the figure is now provided with each individual ModernGraham valuation. In addition, as of today all new valuations will include a chart showing the Graham Number over time in comparison to the stock price. For those investors who place an emphasis on utilizing the Graham Number, this can be a great tool to see how the strategy has performed over time with respect to the specific company. Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Building A Bulletproof Stock Portfolio

Summary An investor can “bullet-proof” his portfolio while maximizing his expected return using the hedged portfolio method. When creating a hedged portfolio, you can start from scratch or start with a list of stock picks. We explore the second method here starting with divided growth stocks. We also provide an example hedged portfolio, designed for an investor unwilling to risk a drawdown of more than 15%. This portfolio has a negative hedging cost. Another Cause For Uncertainty In a recent article (“Investing Alongside Buffett, Klarman and Other Top Investors While Limiting Your Risk”), we mentioned that the reactions to the economic data released Friday exemplified the uncertainty about the current economic environment, centered on the question of whether the Federal Reserve would raise rates soon. However, one of the top trending articles on Seeking Alpha over the weekend (“Something is Still Ridiculously Wrong”) argued that focussing on the when the Fed will raise rates is missing the point. In that article, written a couple of weeks before Friday’s jobs report data was released, Seeking Alpha contribor and mutual fund manager Michael Gayed, CFA, wrote that the bigger concern is that the Fed’s efforts at reflation haven’t helped the real economy, and that could have ominous implications, That is dangerous on many levels, and if the stock market begins to care about the fact that all of these tools central banks are using aren’t actually filtering to the economy, then the future is likely to be extraordinarily more volatile than the past. Dealing With Uncertainty Gayed’s article generated an extraordinary number of comments – 851, as of Monday night – with opinions divided as to his prognosis. One of the top commenters predicted that when his favored candidate is elected President, the stock market will hit new highs. Another top commenter praised Gayed for sounding his warning. Once again, we’re left with the uncertainty that no one knows what direction the market will take from here, and the question of how to invest confidently given that uncertainty. One way to deal with this sort of uncertainty about market direction is to invest in a handful of securities you think will do well, and to “bullet proof” them by hedging against the possibility that you end up being wrong. That approach is systematized in the hedged portfolio method, which we detailed in a previous post (“Backtesting The Hedged Portfolio Method”). An advantage of the hedged portfolio method is that, as our research suggests, it can generate competitive returns over time at a broad range of risk tolerances. Maybe You Can Do Better It’s possible you can get even better returns with the hedged portfolio method by selecting your own securities. And if you’re going to do that, Seeking Alpha can be a good starting point for ideas. For example, Seeking Alpha contributor Chuck Carnevale recently offered an interesting list of dividend growth stocks (“12 Attractive Fast-Growing Dividend Growth Stocks”). For his article, prompted by a question by a younger reader interested more in the potential for dividend growth than current yield, Carnevale screened for companies with above average earnings and dividend growth that he felt were trading currently at attractive valuations. Carnevale’s article included this chart listing the twelve stocks he came up with, along with some of the key metrics he used to screen for them: (click to enlarge) Carnevale’s article is worth a read for some additional color on these stocks and his screening methods and tools. But we’ll start with the assumption that most of these are solid stocks, and we’ll use them as a starting point to construct a hedged portfolio for an investor who is unwilling to risk a drawdown of more than 15%, and has $500,000 that he wants to invest. First, though, let’s address the issue of risk tolerance, and how it affects potential return. Risk Tolerance and Potential Return All else equal, with a hedged portfolio, the greater an investor’s risk tolerance — the greater the maximum drawdown he is willing to risk (his “threshold”, in our terminology) – the higher his potential return will be. So, we should expect that an investor who is willing to risk a 15% decline will have a chance at higher returns than one who is only willing to risk, say, a 5% drawdown. Constructing A Hedged Portfolio In the article about backtesting mentioned above, we discussed a process investors could use to construct a hedged portfolio designed to maximize potential return while limiting risk. We’ll recap that process here briefly, and then explain how you can implement it yourself. Finally, we’ll present an example of a hedged portfolio that was constructed this way with an automated tool. The process, in broad strokes, is this: Find securities with high potential returns (we define potential return as a high-end, bullish estimate of how the security will perform). Find securities that are relatively inexpensive to hedge. Buy a handful of securities that score well on the first two criteria; in other words, buy a handful of securities with high potential returns net of their hedging costs (or, ones with high net potential returns). Hedge them. The potential benefits of this approach are twofold: If you are successful at the first step (finding securities with high potential returns), and you hold a concentrated portfolio of them, your portfolios should generate decent returns over time. If you are hedged, and your return estimates are completely wrong, on occasion — or the market moves against you — your downside will be strictly limited. How to Implement This Approach Finding promising stocks In this case, we’re going to start with Chuck Carnevale’s list of dividend growth stocks. To quantify potential returns for these stocks, you can, for example, use analysts’ price targets for them and then convert these to percentage returns from current prices. In general, though, you’ll need to use the same time frame for each of your potential return calculations to facilitate comparisons of potential returns, hedging costs, and net potential returns. Our method starts with calculations of six-month potential returns. Finding inexpensive ways to hedge these securities First, you’ll need to determine whether each of these top holdings are hedgeable. Then, whatever hedging method you use, for this example, you’d want to make sure that each security is hedged against a greater-than-15% decline over the time frame covered by your potential return calculations (our method attempts to find optimal static hedges using collars as well as protective puts going out approximately six months). And you’ll need to calculate your cost of hedging as a percentage of position value. Selecting the securities with highest net potential returns In order to determine which securities these are, out of the list above, you may need to first adjust your potential return calculations by the time frame of your hedges. For example, although our method initially calculates six-month potential returns and aims to find hedges with six months to expiration, in some cases the closest hedge expiration may be five months out. In those cases, we will adjust our potential return calculation down accordingly, because we expect an investor will exit the position shortly before the hedge expires (in general, our method and calculations are based on the assumption that an investor will hold his shares for six months, until shortly before their hedges expire or until they are called away, whichever comes first). Next, you’ll need to subtract the hedging costs you calculated in the previous step from the potential returns you calculated for each position, and exclude any security that has a negative potential return net of hedging costs. Fine-tuning portfolio construction You’ll want to stick with round lots (numbers of shares divisible by 100) to minimize hedging costs, so if you’re going to include a handful of securities from the sort in the previous step and you have a relatively small portfolio, you’ll need to take into account the share prices of the securities. Another fine-tuning step is to minimize cash that’s leftover after you make your initial allocation to round lots of securities and their respective hedges. Because each security is hedged, you won’t need a large cash position to reduce risk. And since returns on cash are so low now, by minimizing cash you can potentially boost returns. In this step, our method searches for what we call a “cash substitute”: that’s a security collared with a tight cap (1% or the current yield on a leading money market fund, whichever is higher) in an attempt to capture a better-than-cash return while keeping the investor’s downside limited according to his specifications. You could use a similar approach, or you could simply allocate leftover cash to one of the securities you selected in the previous step. Calculating Expected Returns While net potential returns are bullish estimates of how well securities will perform, net of their hedging costs, expected returns, in our terminology, are the more likely returns net of hedging costs. In a series of 25,412 backtests over an 11-year time period, we determined two things about our method of calculating potential returns: it generates alpha, and it overstates actual returns. The average actual return over the next six months in those 25,412 tests was 0.3x the average potential return calculated ahead of time. So, we use that empirically derived relationship to calculate our expected returns. An Automated Approach Here we’ll show an example of creating a hedged portfolio starting with Chuck Carnevale’s twelve fast-growing dividend growth stocks using the general process described above, facilitated by the automated hedged portfolio construction tool at Portfolio Armor . In the first step, we enter the ticker symbols in the “Tickers” field, the dollar amount of our investor’s portfolio (500000), and in the third field, the maximum decline he’s willing to risk in percentage terms (15). In the second step, we are given the option of entering our own return estimates for each of these securities. Instead, in this case, we’ll let Portfolio Armor supply its own potential returns. A couple minutes after clicking the “Create” button, we were presented with the hedged portfolio below. The data here is as of Friday’s close. Why These Particular Securities? The site included all of the entered securities for which it calculated a positive potential return, net of hedging costs. In this case, that turned out to be just two stocks, Apple (NASDAQ: AAPL ), and Gilead Sciences (NASDAQ: GILD ). Since it aims for including six primary securities in a portfolio of this size, and only two of the ones we entered had positive net potential returns, Portfolio Armor included four of the stocks with the highest net potential returns at the time in its universe in the portfolio. Those were Advance Auto Parts (NYSE: AAP ), Alliance Data Systems (NYSE: ADS ), Amazon (NASDAQ: AMZN ), and Regeneron Pharmaceuticals (NASDAQ: REGN ). In its fine-tuning step, Portfolio Armor added Celgene (NASDAQ: CELG ) as a cash substitute. Let’s turn our attention now to the portfolio level summary for a moment. Worst-Case Scenario The “Max Drawdown” column in the portfolio level summary shows the worst-case scenario for this hedged portfolio. If every underlying security in it went to zero before their hedges expired, the portfolio would decline 14.43%. Negative Hedging Cost Note that, in this case, the total hedging cost for the portfolio was negative, -0.96%, meaning the investor would receive more income in total from selling the call legs of the collars on his positions than he spent buying the puts. Best-Case Scenario At the portfolio level, the net potential return is 16.22% over the next six months. This represents the best-case scenario, if each underlying security in the portfolio meets or exceeds its potential return. A More Likely Scenario The portfolio level expected return of 5.62% represents a conservative estimate, based on the historical relationship between our calculated potential returns and backtested actual returns. By way of comparison, if you created a hedged portfolio on Friday using the same dollar amount ($500,000) and decline threshold (15%), but without entering any ticker symbols (i.e., you let Portfolio Armor pick all the securities), the expected return for that hedged portfolio would have been 7.42%. Each Security Is Hedged Note that each of the above securities is hedged. Celgene, the cash substitute, is hedged with an optimal collar with its cap set at 1%; Advance Auto Parts is hedged with optimal puts; and the remaining securities are hedged with optimal collars with their caps set at each underlying security’s potential return. Here is a closer look at the hedge for Gilead Sciences: Gilead is capped here at 5.67%, because that’s the potential return Portfolio Armor calculated for it over the next several months. As you can at the bottom of the image above, the cost of the put protection in this collar is $2,220, or 3.63% of position value. But if you look at the image below, you’ll see the income generated from selling the calls is $3,300, or 5.39% of position value. So, the net cost of this optimal collar is negative.[i] Possibly More Protection Than Promised In some cases, hedges such as the ones in the portfolio above can provide more protection than promised. For an example of that, see this recent instablog post on hedging Tesla (NASDAQ: TSLA ). Hedged Portfolios For Smaller Investors The hedged portfolio shown above was designed for someone with $500,000 to invest, but the same process, with a couple of minor adjustments, can be used for those with smaller amounts to invest. We walked through creating a hedged portfolio for someone with $30,000 to invest in an article last month (“Keeping a Small Nest Egg from Cracking”). [i]To be conservative, this optimal collar shows the puts being purchased at their ask price, and the calls being sold at their bid price. In practice, an investor can often buy the puts for less (i.e., at some point between the bid and ask prices) and sell the calls for more (again, at some point between the bid and ask). So the actual cost of opening this collar would have likely been less (i.e., an investor would have likely collected more than $1080 when opening this hedge). Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Investing Alongside Buffett, Klarman, And Other Top Investors While Limiting Your Risk

Summary An investor can precisely limit his risk while maximizing his expected return by creating a hedged portfolio. When creating a hedged portfolio, you can start from scratch or start with a list of top picks. We lay out the second method here and provide an example. The example hedged portfolio was designed for investors willing to risk a maximum drawdown of 20%. Investors with lower risk tolerances can use a similar process, though their expected returns would likely be lower. Investing In An Uncertain Market Investors could be forgiven for wanting to limit their risk given the uncertainty about the current economic environment. Let’s recap the latest bit of news adding to the uncertainty, and then look at a way we can invest alongside some of the world’s best investors while limiting our risk. Reactions to the August jobs report released on Friday varied. The White House highlighted the positive: Our economy has now added 8.0 million jobs over the past three years, a pace that has not been exceeded since 2000. And while the economy added jobs at a somewhat slower pace in August than in recent months, the unemployment rate fell to 5.1 percent-its lowest level since April 2008-and the labor force participation rate remained stable. And the Wall Street Journal pointed out the dark cloud inside that silver lining: The labor-force participation rate stayed the same last month at 62.6%.The participation rate-the share of the population either working or actively looking for work-has been dropping for several years and is near levels last consistently recorded in the late 1970s, a time when women were entering the workforce in larger numbers. The latest reading is a result of the labor force shrinking by 41,000 last month, despite other signs of an improving jobs market. As the New York Times noted , the jobs report gave ammunition to both sides of the Fed rate debate, but, as Seeking Alpha news editor Carl Surran summarized it, the market’s verdict seemed to be negative, with the major market indexes down on Friday and all ten sectors in the red. Dealing With Uncertainty After all the analysis, no one knows what direction the market will take from here. One way to deal with uncertainty about market direction is to invest in a handful of securities you think will do well, and hedge against the possibility that you end up being wrong. That approach is systematized in the hedged portfolio method, which we detailed in a previous post (“Backtesting The Hedged Portfolio Method”). One advantage of the hedged portfolio method is that it can accommodate a broad range of risk tolerances. If you can tolerate a drawdown of more than 20%, our research (summarized in the previous post we mentioned above) suggests that with our security selection method you can achieve returns as good or better than the market over time with less risk. Maybe You Can Do Better It’s possible you can get even better returns with the hedged portfolio method by selecting your own securities. And if you’re going to do that, a good starting place for ideas is to look at what some of the best investors in the world have been buying. Seeking Alpha contributor and hedge fund manager Chris DeMuth, Jr. did just that in a recent article (“Best Q2 Picks From Top Investors”). In that article, DeMuth examined reported buys from leading investors and highlighted a number of them. These were the stocks, along with the investors who bought them: SunEdison Semiconductor (NASDAQ: SEMI ) – Seth Klarman. Precision Castparts (NYSE: PCP ) – Warren Buffett SunEdison (NYSE: SUNE ) – David Einhorn Perrigo (NYSE: PRGO ) – Stephen Mandel (former analyst for Julian Robertson) Williams (NYSE: WMB ) – Dan Loeb Danaher (NYSE: DHR ) – John Griffen (another former protege of Julian Robertson) Time Warner Cable (NYSE: TWC ) – John Paulson Baker Hughes (NYSE: BHI )- Jeff Ubben Shire (NASDAQ: SHPG ) – Leon Cooperman Office Depot (NASDAQ: ODP ) – Richard Perry Humana (NYSE: HUM ) – Larry Robbins Cigna (NYSE: CI ) – Andreas Halvorsen Altera (NASDAQ: ALTR ) – Andrew Spokes Icahn Enterprises (NASDAQ: IEP ) – Carl Icahn Brookdale Senior Living (NYSE: BKD ) – Barry Rosenstein T-Mobile (NYSE: TMUS ) – Phillippe Lafont DeMuth’s article is worth a read for some color on these stocks and investors (particularly, the less well-known investors). But we’ll start with the assumption that most of these are solid stocks, and we’ll use them as a starting point to construct a hedged portfolio for an investor who is unwilling to risk a drawdown of more than 20%, and has $1 million he wants to invest. First, though, address the issue of risk tolerance, and how it affects potential return. Risk Tolerance and Potential Return All else equal, with a hedged portfolio, the greater an investor’s risk tolerance — the greater the maximum drawdown he is willing to risk (his “threshold”, in our terminology) – the higher his potential return will be. So, we should expect that an investor who is willing to risk a 20% decline will have a chance at higher returns than one who is only willing to risk, say, a 10% drawdown. Constructing A Hedged Portfolio In the previous article mentioned above, we discussed a process investors could use to construct a hedged portfolio designed to maximize potential return while limiting risk. We’ll recap that process here briefly, and then explain how you can implement it yourself. Finally, we’ll present an example of a hedged portfolio that was constructed this way with an automated tool. The process, in broad strokes, is this: Find securities with high potential returns (we define potential return as a high-end, bullish estimate of how the security will perform). Find securities that are relatively inexpensive to hedge. Buy a handful of securities that score well on the first two criteria; in other words, buy a handful of securities with high potential returns net of their hedging costs (or, ones with high net potential returns). Hedge them. The potential benefits of this approach are twofold: If you are successful at the first step (finding securities with high potential returns), and you hold a concentrated portfolio of them, your portfolios should generate decent returns over time. If you are hedged, and your return estimates are completely wrong, on occasion — or the market moves against you — your downside will be strictly limited. How to Implement This Approach Finding promising stocks In this case, we’re going to start with the list of Q2 best picks curated by Chris DeMuth. To quantify potential returns for these stocks, you can, for example, use analysts’ price targets for them and then convert these to percentage returns from current prices. In general, though, you’ll need to use the same time frame for each of your potential return calculations to facilitate comparisons of potential returns, hedging costs, and net potential returns. Our method starts with calculations of six-month potential returns. Finding inexpensive ways to hedge these securities First, you’ll need to determine whether each of these top holdings are hedgeable. Then, whatever hedging method you use, for this example, you’d want to make sure that each security is hedged against a greater-than-20% decline over the time frame covered by your potential return calculations (our method attempts to find optimal static hedges using collars as well as protective puts going out approximately six months). And you’ll need to calculate your cost of hedging as a percentage of position value. Selecting the securities with highest net potential returns In order to determine which securities these are, out of the list above, you may need to first adjust your potential return calculations by the time frame of your hedges. For example, although our method initially calculates six-month potential returns and aims to find hedges with six months to expiration, in some cases the closest hedge expiration may be five months out. In those cases, we will adjust our potential return calculation down accordingly, because we expect an investor will exit the position shortly before the hedge expires (in general, our method and calculations are based on the assumption that an investor will hold his shares for six months, until shortly before their hedges expire or until they are called away, whichever comes first). Next, you’ll need to subtract the hedging costs you calculated in the previous step from the potential returns you calculated for each position, and exclude any security that has a negative potential return net of hedging costs. Fine-tuning portfolio construction You’ll want to stick with round lots (numbers of shares divisible by 100) to minimize hedging costs, so if you’re going to include a handful of securities from the sort in the previous step and you have a relatively small portfolio, you’ll need to take into account the share prices of the securities. Another fine-tuning step is to minimize cash that’s leftover after you make your initial allocation to round lots of securities and their respective hedges. Because each security is hedged, you won’t need a large cash position to reduce risk. And since returns on cash are so low now, by minimizing cash you can potentially boost returns. In this step, our method searches for what we call a “cash substitute”: that’s a security collared with a tight cap (1% or the current yield on a leading money market fund, whichever is higher) in an attempt to capture a better-than-cash return while keeping the investor’s downside limited according to his specifications. You could use a similar approach, or you could simply allocate leftover cash to one of the securities you selected in the previous step. Calculating Expected Returns While net potential returns are bullish estimates of how well securities will perform, net of their hedging costs, expected returns, in our terminology, are the more likely returns net of hedging costs. In a series of 25,412 backtests over an 11-year time period, we determined two things about our method of calculating potential returns: it generates alpha, and it overstates actual returns. The average actual return over the next six months in those 25,412 tests was 0.3x the average potential return calculated ahead of time. So, we use that empirically derived relationship to calculate our expected returns. An Automated Approach Here we’ll show an example of creating a hedged portfolio starting with Chris DeMuth’s best Q2 picks using the general process described above, facilitated by the automated hedged portfolio construction tool at Portfolio Armor . In the first step, we enter the ticker symbols in the “Tickers” field, the dollar amount of our investor’s portfolio (1000000), and in the third field, the maximum decline he’s willing to risk in percentage terms (20). In the second step, we are given the option of entering our own return estimates for each of these securities. One of these securities, PCP, appeared in a hedged portfolio in a previous article (“An Alternative To Cash For A Risk Averse Investor), and there, we used Portfolio Armor’s calculated potential return for it. In this case, for illustration purposes, we’ll enter a potential return for it based on the assumption that the Berkshire Hathaway deal closes at the announced price of $235 per share. For the other securities, we’ll let Portfolio Armor supply its own potential returns. A couple minutes after clicking the “Create” button, we were presented with the hedged portfolio below. The data here is as of Friday’s close. Why These Particular Securities? The site included all of the entered securities for which it calculated a positive potential return, net of hedging costs. Interestingly, one of the stocks it rejected, Icahn Enterprises , is one Chris DeMuth mentioned as a short position earlier this year, as he noted in his Best Q2 Picks article. In its fine-tuning step, Portfolio Armor added Google (NASDAQ: GOOG ) as a cash substitute. Let’s turn our attention now to the portfolio level summary for a moment. Worst-Case Scenario The “Max Drawdown” column in the portfolio level summary shows the worst-case scenario for this hedged portfolio. If every underlying security in it went to zero before the hedges expired, the portfolio would decline 19.67%. Negative Hedging Cost Note that, in this case, the total hedging cost for the portfolio was negative, -1.03%, meaning the investor would receive more income in total from selling the call legs of the collars on his positions than he spent buying the puts. Best-Case Scenario At the portfolio level, the net potential return is 13.44% over the next six months. This represents the best-case scenario, if each underlying security in the portfolio meets or exceeds its potential return. A More Likely Scenario The portfolio level expected return of 4.63% represents a conservative estimate, based on the historical relationship between our calculated potential returns and backtested actual returns. However, since these securities are picks of some of the world’s best investors, it’s possible Portfolio Armor is underestimating their returns over the next six months. By way of comparison, if you created a hedged portfolio on Friday using the same dollar amount ($1,000,000) and decline threshold (20%), but without entering any ticker symbols (i.e., you let Portfolio Armor pick the securities), the expected return for that hedged portfolio would have been 7.97%. That hedged portfolio would have only had one primary security in common with this one; as you can probably guess from the potential returns shown in the hedged portfolio above, that security was Advance Auto Parts. Each Security Is Hedged Note that each of the above securities is hedged. Google, the cash substitute, is hedged with an optimal collar with its cap set at 1%; Advance Auto Parts and Precision Castparts are hedged with optimal puts; and the remaining securities are hedged with optimal collars with their caps set at each underlying security’s potential return. Here is a closer look at the hedge for Advance Auto Parts: The cap field above is blank, because this isn’t a collar. Portfolio Armor used optimal puts in this case instead of an optimal collar because the position had a higher net potential return this way (it calculated the net potential returns both ways for each of the primary positions in the portfolio). As you can see at the bottom of the image above, the cost of this hedge was $2,500, or 2.90% of position value.[i] Note that, although this hedge had a positive hedging cost, the hedging cost for the portfolio as a whole was negative. Possibly More Protection Than Promised In some cases, hedges such as the ones in the portfolio above can provide more protection than promised. For an example of that, see this recent instablog post on hedging Tesla (NASDAQ: TSLA ). Hedged Portfolios For Smaller Investors The hedged portfolio shown above was designed for someone with $1 million to invest, but the same process, with a couple of minor adjustments, can be used for those with smaller amounts to invest. We walked through creating a hedged portfolio for someone with $30,000 to invest in an article last month (“Keeping a Small Nest Egg from Cracking”). [i] To be conservative, the cost of the put protection was calculated using the ask price of the puts. In practice, an investor can often buy puts for less than the ask price (i.e., at some price between the bid and ask). So, in practice, an investor would likely have paid less than $2,880 for this hedge. A similarly conservative approach was used for calculating the costs of all of the hedges in this portfolio (with the cost of puts calculated at the ask and the income from calls calculated at the bid). Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.