A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing

by Burton G. Malkiel

There is a fundamental paradox about the usefulness of investment advice concerning specific securities. If the advice reaches enough people and they act on it, knowledge of the advice destroys its usefulness. If everyone knows about a “good buy” and everyone rushes in to buy, the price of the “good buy” will rise until it is no longer a good buy.

Perhaps the finance professor’s advice should have been, “You had better pick up that $100 bill quickly because if it’s really there, someone else will surely take it.” It is in this sense that I consider myself a random walker. I am convinced that true value will out, but from time to time it doesn’t surprise me that anomalies do exist. There may be some $100 bills around at times, and I’ll certainly interrupt my random walk to stoop and pick them up.

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too. It’s much too much fun to give up. If you have the talent to recognize stocks that have good value, and the art to recognize a story that will catch the fancy of others, it’s a great feeling to see the market vindicate you. Even if you are not so lucky, my rules will help you limit your risks and avoid much of the pain that is sometimes involved in the playing. If you know you will either win or at least not lose too much, and if you index at least the core of your portfolio, you will be able to play the game with more satisfaction. At the very least, I hope this book makes the game all the more enjoyable. A FINAL WORD One

The system, explained more fully below, became known as the futures market and was centered in Chicago. Because of that city’s historical association with the processing and sale of sides of beef and pork, the catchy commodity component “pork belly” was used as a bellwether for all commodity futures trading. If the price of pork bellies went up, traders on LaSalle Street smiled; if it sank, they grimaced.

Derivatives are simply financial instruments whose value is determined by (or “derived” from) the price of some underlying asset, such as stocks, bonds, currencies, or commodities. As we shall see below, what they do is permit the transfer of risks and broaden the investment and hedging opportunities available to individuals and institutions. They also provide the means to undertake highly leveraged speculative positions.

The two most popular forms of financial derivative securities are futures and options contracts. They are derivatives because they take their value from their connected underlying securities. While we will concentrate on simple options and futures, it should be noted that many other derivative-type instruments build upon these two basic forms. These complex derivatives have fancy and often forbidding names, such as swaps, inverse floaters, leaps, lookbacks, swaptions, quantos, rainbows, floors, caps, and collars.

A burgeoning market exists in financial futures, where one can buy for future delivery a variety of bonds, currencies, and stock-market indexes such as the S&P 500. These financial futures are typically settled in cash on the basis of the difference between the initial contract price and the final cash market price of the financial instrument. No physical delivery is made.

For example, a call option on IBM might cost the buyer $15 a share (the option premium) expiring the third Friday in July (the expiration date) with an exercise price of $150 a share (the striking price). Thus, for a premium of $15, the buyer of this call option has the right to purchase a share of IBM at $150 at any time up through the third Friday in July. The seller (or writer) of the option receives the premium and takes on the corresponding potential obligation to sell the share at the contract price. A put option reverses the situation. A put on IBM gives the holder the right to sell IBM shares at a specific price. The seller of the put (called the writer) takes on the potential obligation to buy the shares.

The volume of trading in basic options and futures has actually exceeded the volume of trading in the underlying assets. What makes the market important, however, is not simply its size but also the significant role it plays in providing new tools to manage risk.

During the early stages of the development of American agriculture, grain prices were subject to seemingly perpetual cycles of boom and bust, as prices fell when farmers flooded the market with grain at harvest time and then rose later as shortages developed. Buyers and sellers began to contract for future delivery of specific quantities of grain at agreed-upon prices and delivery dates. These “to arrive,” or forward, contracts were themselves bought and sold in anticipation of changes in market prices and became the basis for the standardized futures contracts traded on the Chicago Board of Trade, the first organized commodities futures market in the United States.

What the Hunts did was quite simple—and quite daring. They cornered the silver market by accumulating gigantic positions in the futures market to buy silver and then demanding delivery when the contracts came due. Simultaneously, they accumulated enormous stocks of silver in the spot market (the market in which physical quantities of the metal were bought for immediate delivery) and held this silver off the market, making it difficult for those who had sold silver futures to fulfill their obligations. Thus, they increased demand in the futures market while restricting supply in the spot market. The price of silver skyrocketed.

Corners have been a fact of life in the commodities markets since their inception, and so has the attempt at regulation. In the United States, the Commodity Futures Trading Commission (CFTC) attempts to avoid corners by ensuring that there are limits on the amount of futures contracts any individual or group can hold.

the full settlement was never collected against the Hunts. The two brothers—the world’s richest men at the outset of the 1980s—sought protection in bankruptcy in 1990. So ended one of history’s greatest corners of a commodities market.

These newer contracts also incorporated the feature of cash settlement. Thus, if one bought a futures contract on the S&P 500-Stock Index at a price of $2,000, the seller would not deliver a package of the 500 stocks on the expiration date. Rather, the contract would be settled in cash on the basis of the difference between $2,000 and the value of the index on the settlement date. Today, trading in financial futures represents well over half of the total futures trading.

When you buy a $100,000 position in Treasury bonds for future delivery, you may have to put up an initial margin of as little as $1,000. But if the Treasury securities suddenly drop in price by just 2 percent, a movement that could happen in a single day, you will be liable for a loss of $2,000, double the amount of your initial capital.

Suppose, for example, you believed that the prices of stocks of smaller companies would rise relative to stocks of larger companies. You might buy a three-month future on the Russell 2000 index (an index of smaller firms) and sell an equivalent futures contract on the S&P 500 (an index of the biggest companies). Note that you would be hedged in the sense that if all stocks went down, you would lose on your Russell 2000 contract but gain on the S&P contract. As long as small stocks did better than large stocks on a relative basis, you could gain whatever the direction of the general market. However, if the relative performance figures went the other way—that is, big-company stocks did better than small-company stocks—you could lose substantial sums of money. This is so because futures markets allow you to control billions of dollars worth of securities while putting up a security deposit of only millions. Derivatives truly provide investors with staggering amounts of leverage.

Another factor to keep in mind is that derivative transactions can entail substantial trading costs. If an option is quoted as 5 bid–5¼ asked, it means you buy the option at 5¼, whereas if you sell it, you get only 5. That ¼ point spread is a 5 percent transactions charge on the purchase or sale of that particular instrument (a so-called round-trip transaction) and does not include brokerage commissions.

After two years of operation, the participants in the club graduated and divided their spoils. The final accounting showed that the original $2,000 had grown to $2,125 for an annual rate of return of approximately 3 percent. This was far below the 10 percent rate of return for the stock market as a whole over the same period. How could such brilliant pickers underperform the market? The answer: transaction costs, pure and simple. These totaled $980, almost 50 percent of their original stake. The budding entrepreneurs had done more to fatten the coffers of the financial community than to contribute toward their tuition bills.

Leverage, as we all know, works two ways. Let’s continue the example where the investor puts all $4,000 into call options, and let’s suppose that Halliburton doesn’t move within the three-month option period. The stock buyer still has his original stake intact and has lost nothing. Indeed, he has collected any dividends paid out during the three-month period. The option buyer, however, receives no dividends and has lost $4,000, 100 percent of his investment.

Option buyers have to be right not only on the direction of the movement in the stock but also on the exact timing of when the move will take place. If Halliburton makes its move in four months, an option buyer can still lose everything, whereas the stock buyer would be fully rewarded. Before you engage in an options-buying strategy, consider how difficult it is not only to pick the right stock but also to time its upward move perfectly.

Thus, a put-option buyer profits only if the stock declines—and declines by more than the option premium. For example, if the put option costs $4 per share, the put option buyer will not make any money until the price of Halliburton stock falls below $36 a share.

There is another way to gain some protection against a fall in the price of Halliburton. The owner of the stock can sell (write) a call against his position. This is called “covered” call writing and is explained in chart 3.

If the price of Halliburton stock stays within 20 percent of the starting price within the three-month period, you are much better off selling a call option on the stock and collecting the premium as opposed to paying for a put. Indeed, even if the price of Halliburton declines to $32, a 20 percent decline, you are in exactly the same position using either strategy. Thus, as long as you think Halliburton will sell within a range of plus or minus 20 percent within a three-month period, writing covered calls offers some protection and is never a poorer strategy. Only if Halliburton stock rises or falls more than 20 percent would put buying be better. The put-buying strategy produces more protection against very severe price declines and allows the investor to profit more in the event of a very large price increase.

Selling a call option without owning the stock is called naked call writing. Remember that the call writer receives a lump sum for taking on the potential obligation to deliver 100 shares of stock to the option buyer at a set striking price (in all our examples, $40). Thus, if the stock price goes to $60, $1,600 goes out the window for the writer of a 100-share contract. The naked call writer must spend $6,000 to obtain 100 shares of Halliburton, which then must be turned over to the option buyer at the guaranteed price of $4,000. That $2,000 difference, minus the $400 option premium, makes up the $1,600 loss.

It is clear, however, that naked writing is a very risky strategy. If the options remain unexercised, the gains to the writer are extremely large. But the potential losses can be staggering. Writers of naked puts were the ones who lost everything during the crash of 1987 and the sharp decline during 2008, while writers of naked calls lost heavily during the late 1990s when stock prices were soaring.

Both purchasers and sellers of futures contracts are subject to margin requirements, which determine both the initial deposit and the maintenance level. Not only that, financial futures have a special pay-as-you-lose system. At the end of each trading day, the value of a futures contract is determined and the party suffering the loss pays that loss to the gainer. (This is called marking to market.) Thus, whether a buyer or a seller of a financial futures contract, you must pay all losses as they accrue. Unless a trader closes out his futures position, he would be required, in the event of an uninterrupted market slide, to continue to pay unrealized losses as they occurred.

investor who was very confident about the prospects for her stock holdings, but very nervous about the overall level of stock prices, might sell S&P futures in the hope that even if the stock market declined sharply, the profit from the sale of the futures would exceed the losses from any individual stock holdings.

the squealing by players losing heavily in the derivatives markets led some regulators and politicians to worry aloud about the potential fragility of the whole financial system. While trading in standardized options and futures is centrally cleared and guaranteed by well-capitalized clearing corporations, individually designed derivatives are simply bilateral transactions between buyer and seller. These customized derivatives are the ones responsible for the large losses suffered by many market participants during the 1990s and during the financial crisis of 2007–08.

Institutions wishing to change a portfolio’s equity mix or hedge against market declines can do so more quickly and at lower transactions costs in the futures market than in the underlying securities markets. This is why futures markets often react to new information first and give the impression that they cause price movements in the stock market.

Blaming futures and related program trading for the volatility in the stock market is as illogical as blaming the thermometer for measuring uncomfortable temperatures. By making the market more quickly responsive to changes in underlying conditions or the sentiment of large institutions, rapid trading increases the efficiency of the stock market. To eliminate new instruments and techniques would be to make our markets less efficient.

Yes, sudden large movements in stock prices are upsetting to individual investors who feel at the mercy of large institutional traders. But to paraphrase a common expression, “If you can keep your head when those around you are losing theirs, you do understand the problem.” The long-term investor can and should ignore short-term market volatility and not leave the stock market. The losers from volatility will be institutions that trade frequently in a futile attempt to time the market, not the steady investor who buys and holds for the long term.

I recognize, however, that many investors, particularly those with a gambling temperament, will not be satisfied unless they do some picking of individual stocks. If you are one of these people, you might want to commit 95 percent of your funds to index mutual funds and ETFs and speculate with the remaining 5 percent. The options market allows you to buy a few positions for a moderate amount of money and the odds there are certainly better than at either the race track or your state lottery. Be prepared to lose your entire 5 percent stake because that is a real possibility, and take to heart the lessons of the Princeton Students Investment Club. You may well enrich only your broker by undertaking an option-buying strategy. Moreover, your gains, if any, will be taxed at ordinary income tax rates. And never forget, you are gambling and not investing.

Option writing gave Dr. Brown a way out of her dilemma. She began a program of writing call options of approximately three months in length “at-the-money,” that is, with a striking price at or about the then current market price of $70. For this, she received an option premium of about $6 per share, or about 8½ percent of the market price.

The main determinants of option premiums “at-the-money” are (1) the stock’s characteristic volatility and (2) the length of time the option runs.

At the end of the three-month period, the price of Merck stock remained at about $70. The option expired unexercised, and Dr. Brown then wrote (sold) another three-month call option for $600. At the end of the next period, her fears began to be realized. The price of Merck fell to $60, and again the option remained unexercised. Dr. Brown in effect lost $10 per share in the market value of the stock but pocketed the $600 option premium as well as the generous quarterly dividend paid by Merck. Hence, she largely avoided the loss she would have suffered if she had taken no offsetting action in the options market.

Futures prices depend on the interest rate and storage costs. One additional factor is likely to enter the equation—the so-called “convenience yield” of having the inventory directly on hand. In general, the futures price will be above the spot price because of the interest and storage factors, but it could in some circumstances be lower when the convenience yield is very high, as might happen if the commodity was in very short supply.

The higher the exercise price, the lower the value of the option. Of course, the value of the option can never go below zero. As long as there is some probability that the market price of the stock can exceed the exercise price in the future, the option will have some value.

The longer the option has to run, the greater its value.

The greater the volatility of the underlying stock in question, the higher the cost of a call option. An at-the-money call on Halliburton, an extremely volatile stock, is likely to sell for very much more than an at-the-money call of similar length on a more stable stock such as AT&T.

Call prices are also a function of the level of interest rates. The buyer of a call option does not pay the exercise price until and unless he exercises the option. The ability to delay payment is more valuable when interest rates are high and, therefore, earnings opportunities on cash are very attractive.

Although the mathematics behind the Black-Scholes model will be inaccessible for most readers, a related model—the binomial model—can be easily understood by anyone familiar with high school algebra. Moreover, the general insights that inform Black-Scholes can all be found in the binomial model. Indeed, a multiperiod binomial model produces results equivalent to those of Black-Scholes.

If the stock rises, the call buyer exercises her option and presents $100 to buy a share of stock. The writer is obligated to deliver a share, but he owns only ⅔ of a share. Hence the writer must purchase ⅓ share at the then current price of $150. This costs him $50, for a net payoff of $50. If the stock falls to $75, the call is not exercised and the investor is left holding ⅔ of a share of a $75 stock, which is also worth $50. Thus, the investor has a final payoff of $50, irrespective of whether the stock rises or falls, and is thus perfectly hedged.

DETERMINATION OF HEDGE RATIO

ILLUSTRATION OF THE DETERMINATION OF THE VALUE OF A CALL OPTION Amount Invested (1+ Risk-Free Interest Rate) = Certain Payoff [Hedge Ratio (Initial Stock Price) – C](1+ Interest Rate) = Certain Payoff [⅔(100) – C](1+.10) = 50 (66.67 – C)(1.1) = 50 C = 21.22

We assumed that only two outcomes were possible after one year. But suppose we consider a two-stage (six-month) binomial model. After the first six months, the stock can go up or down. After the second six months, again two outcomes are possible. This leads to three possible outcomes at the end of one year. The stock can go up in both periods or down in both. Alternatively the stock could rise (fall) in the first period and fall (rise) in the second. Thus, three outcomes are possible. We could also do a four-stage binomial model where each quarter the stock price could rise or fall and several different outcomes would be possible. Or we could do a daily binomial or even an hourly or minute-by-minute model. As we break the binomial model into finer and finer subperiods, the binomial model and the Black-Scholes model converge.