portfolio insurance and market volatility

CFA Institute

Portfolio Insurance and Market VolatilityAuthor(s): Jack L. TreynorSource: Financial Analysts Journal, Vol. 44, No. 6 (Nov. - Dec., 1988), pp. 71-73Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4479170 .

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half the plan's equity exposure ($100 million) in an index fund based on the Standard & Poor's 500. Because the plan again "borrows" at the cash-equiva- lent rate implicit in futures contracts, the expected return on Strategy III is similar to the return on Strategy II. The use of corporate bonds, however, allows Strategy III to increase its expected return over that of Strategy II. Table VI summarizes the strategy.

The major advantages of Strategy III over Strategy II are:

* The bonds are real, which means the plan can maximize fixed income returns while minimizing basis and mismatching risks by selecting a diver- sified portfolio of corporate and government bonds.

* The futures have been used to create synthetic

equity instead of synthetic bonds. While some basis risk remains, by design equity futures track the S&P 500 much more precisely than bond futures track liability-matching bonds.

Thus plan sponsors may use dollar-duration matching to (1) increase their expected returns, (2) reduce surplus and expense volatility and (3) main- tain their equity exposure. Those who elect to do so without using futures will accomplish most of their objectives. Plan sponsors who use fixed income futures will be better able to match the liabilities and will add to their expected returns. Those who use equity futures will add to these advantages the ability to match liabilities using a much broader universe of bonds, including corporate bonds instead of zero coupon bonds and fixed income futures.

Portfolio Insurance and Market Volatility

by Jack L. Treynor, Treynor Capital Management, Inc.

The key to understanding why the Black Monday crash was so deep is the model of dealer behavior described in "The Economics of the Dealer Func- tion."* That model distinguishes between two fundamentally different kinds of investors, who transact with dealers in fundamentally different ways:

* The information-motivated transactor (IBT) is in a hurry to transact before this information gets impounded in price. Investors who believe, rightly or wrongly, that they have information are one of the dealer's most important customers. They are sufficiently anxious to transact that they pay a price of the dealer's choosing in order to transact at a time of their choosing.

* The value-motivated transactor (VBT) is a bar- gain hunter. When he perceives a big enough discrepancy between price and value, he trans- acts. In no hurry to transact, he waits until someone meets his price.

In a market without dealers, transactors in a hurry would trade with value-based transactors, paying whatever difference between price and value (perhaps 15 to 20 per cent) is required to motivate the VBT to trade. The function of the dealer is to intermediate between buyers in a hurry and sellers in a hurry, sparing both the high cost of trading with the VBT.

Even if buy and sell orders arrive randomly (as indeed they will if the dealer's price is close to the equilibrium price), the dealer will experience runs of buys and runs of sells. Because the dealer accommo-

dates his customers by transacting for his own ac- count, these runs result in big changes in his own position. When the dealer's position gets too long or short for comfort, he lays off or buys in from the only investor willing to transact at a time of someone else's choosing-the value-based transactor. To do so, of course, the dealer must meet the VBT's price.

To avoid accommodating a customer at one price and turning around and laying off (or buying in) at a different, less favorable price, the dealer adjusts his own price to reflect the likelihood of his having to lay off or buy in-which is to say, to reflect his position. Thus the dealer's price can range from the VBT's bid when the dealer is close to laying off to the VBT's ask when the dealer is close to buying in-a range of perhaps 30 to 40 per cent of the security's value- without any change in the VBT's appraisal of the true value.

Enter the portfolio insurer (PI). His trading behavior differs from that of either the IBT or the VBT. Unlike the IBT, he is price, rather than information, motivated. But unlike the VBT, who is also price- motivated, he is in a hurry to trade because he needs to track market-level changes fairly closely. And his trading behavior is unique in that he buys when price rises and sells when it falls.

Professor Hayne Leland of the University of Cali- fornia at Berkeley (and a principal of Leland O'Brien Rubinstein, purveyors of portfolio insurance) was quoted in the New York Times as arguing that, even with $60 to $90 billion in assets, portfolio insurance had an insignificant impact on equilibrium prices, compared with the impact of orthodox investors (with their $1,000 to $2,000 billion). The problem with this argument is that, within the widely separated prices at which the enormous assets of VBTs come into play, there are, broadly speaking, only three kinds of transactors:

* information-based and other non-price-motivated transactors in a hurry;

* J.L. Treynor, "The Economics of the Dealer Function," Financial Analysts Journal, November/December 1987.

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 a 71



* portfolio insurers, who are price-motivated, but perversely; and

* dealers, whose price rises as their position falls and falls as their position rises.

In adjusting their portfolios to changing market levels, portfolio insurers do not distinguish-indeed, cannot distinguish-between changes in equilibrium price and changes in dealer price due purely to changes in dealer position. A drop in the dealer's position leads to an increase in the dealer's price, to which the portfolio insurer responds by quickly buying more, lowering the dealer's position still further, and so on. The result of this process, which under certain circumstances can be unstable, is an increase in the volatility of dealer price. (The effect is obvious- ly symmetric.)

Calculating the Impact To explore the impact of portfolio insurance on

price volatility, let

x = the combined holdings of portfolio insurers and dealers (stock and futures combined),

xl = the dealer's position, x2 = the portfolio insurer's position, p* = the fair price according to value-based inves-

tors, and p = the mean of the dealer's current bid and ask

prices.

For the dealer, a long position corresponds to a mean dealer price p low in relation to p*-what value-based investors think the security is worth. For some positive constant XI, therefore, we have:

XI = -X1(p - p*). (1)

But the higher the price level p, the more shares (or share equivalents) portfolio insurers want to hold. For another positive constant X2 we have, then:

dx,2 -dx = X2. (2) dp

From our definition of x we have

x = xI + X2. (3)

These three equations determine the behavior of dealer price p as a function of the demands of the dealer's other customers as reflected in x and the value p* of the security according to value-based investors. Differentiating the first and third equations with respect to p we have

dx= - XI (4) dp

and

dx dx1 dx2 dp dp dp (5)

respectively. Substituting Equations (2) and (4) in Equation (5), we have:

dx dp 1 _=-Xl + X2; - =(6) dp dx X- X2

When X2 is zero, this result simplifies to Equation (4); in the absence of portfolio insurance, price sensitivity to trading pressure is the same as if the dealer were functioning alone.

Recalling that XI and X2 are both positive, we can see that as portfolio insurance catches on, and X2 grows, the sensitivity of dealer price to net demands for rapid accommodation also grows, blowing up when:

X2 = X1.

What about the response of dealer price p to changes in the value-based transactor's estimate of value p*? Differentiating Equations (1) and (3) with respect to p*, we have, respectively

dx1 I dp XI ,(7)

dp* dp* / and

dx1 dx2 - + = 0, (8)

dp* dp*

noting that x is unaffected by a change in p*. Substi- tuting from Equation (8) into Equation (7), we have:

dx2 _ dp _~ = -XI dp* dp*

dx2 dp dp

dp dp* dp*

Substituting from Equation (2), we have:

dp dp XI 1 - A2 XIA,

dp* dp*

dp XIl_9_ dp* XI - X2

Absent portfolio insurance, X2 is zero, and the change in dealer price (excluding effects of dealer position) equals the change in the value-based investor's appraisal. As portfolio insurance catches on, X2 increases. The denominator falls (as previously noted, XI and X2 are always positive), and the value of the fraction rises. Dealer price p becomes more vola- tile, blowing up when X2 equals XI.

As noted, portfolio insurance at its apogee con- trolled $60 to $90 billion of assets. NYSE specialist firms control perhaps $1 to $2 billion. Does this mean

Xzwas not merely equal to Xl, but far larger? No,

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 I 72



because the specialist commits a vastly larger fraction of his capital for a given price change than the portfolio insurer does.

Does a blow-up in the volatility of dealer price mean market chaos? No-it only means that the

dealer price oscillates between the value-based transaction's bid and ask. Still, given a 30 to 40 per cent spread between the outside bid and ask, the resulting price volatility will be spectacular-as indeed it was on Black Monday.

The S&P 500 Membership Anomaly, or Would You Join this Club?

by William E. Jacques, Partner, Martingale Asset Man- agement *

If you have had money invested in an S&P 500 index fund, congratulations! You have been the bene- ficiary of one of the most consistently successful active strategies of the 1980s. A recent study by Martingale Asset Management and BARRA reveals that stocks belonging to the S&P 500 produced ap- proximately 4.0 per cent per year of extra return compared with non-index companies with similar characteristics.' The phenomenon seems to be accel- erating, with membership worth an extra 6 per cent for 1987 alone. The dramatic surge in indexing to the S&P 500 appears to be one of several trends that have turned the S&P 500 members into the "Nifty 500," the new one-decision stocks of the 1980s.

During the late 1960s and early 1970s, rising prices of large, high-quality growth stocks seemed to pos- sess unstoppable momentum. As prices of these stocks rose higher and higher, investors devoted to the growth stock style developed a rationale to de- fend the escalating P/E ratios: "It doesn't matter what you pay to buy shares in one of the Nifty 50, because you will never have to sell them." Hence the label one-decision stocks. Investors thought the high rates of earnings growth were so certain that any price paid for these stocks would eventually be justified. The Nifty 50 peaked in early 1973 and by the end of 1974 were selling at a fraction of their former highs. They were the worst casualties in the biggest bear market since the 1930s. Will the current fascination with the 500 stocks in the S&P 500 end the same way?

What's Going On? By the late 1970s, growing acceptance of efficient

market theory legitimized indexing as an investment strategy for institutional clients. (Figure A shows cumulative excess return associated with the S&P 500 factor emerging towards the end of 1979.) Over the

past decade, equity money indexed directly to the S&P 500 has grown from several billion dollars to upwards of $200 billion.2 As active equity managers lost market share to index funds, non-S&P 500 stocks were sold to make room for S&P 500 purchases. Not only was buying pressure placed on index members, but selling pressure was exerted in a less liquid sector of the market.3

A more subtle version of buying pressure on the S&P 500 members was generated during the 1980s by closet indexers. Closet indexers are those institutional investors who feel compelled to construct portfolios whose results will be unlikely to deviate far from the S&P 500 index. Many clients monitor results closely and replace managers who significantly lag the index. Client interest in the S&P 500 as a performance benchmark has grown as roughly two-thirds of all active managers failed to match the index in each of the last five years.4

The best formula for success in the investment management business has not been top performance. The secret has been to avoid bringing up the rear. The penalty for being your client's worst-performing manager far outweighs the reward for being the best. Consequently, many active investment managers brought their portfolios closer to the "market" by purchasing more S&P 500 stocks, thus reinforcing the actions of the true index managers.

Investing in the S&P 500 became easier in 1982, when trading in S&P 500 index futures began. No one appreciated then just how much these derivative instruments would eventually affect trading in the underlying stocks. For the first time, investors could buy and sell a package of S&P 500 stocks with a very low transaction cost. Volume grew rapidly, and arbi- trageurs were attracted to buy and sell the underlying stocks to align the futures and cash markets. S&P 500 futures trading brought a higher level of liquidity to these stocks. Investors generally prefer liquidity and, as usual, were willing to pay a premium for what they liked.

While all the domestic forces mentioned above would surely have been sufficient to create the S&P membership anomaly, foreign investors provided the finishing touch. A weak dollar combined with trade surpluses dramatically increased the flow of investment into U.S. markets. From their perspective, foreign investors can purchase "name brand" companies for less, and the S&P 500 has become their shopping list. The S&P 500 has become an exclusive club, and investors seem willing to pay their dues to

5 join.

1. Footnotes appear at end of article.

*The author thanks John D. Freeman, Manager of Consulting at BARRA, whose work contributed greatly to this piece, and Arnold Wood, Alan Strassman, Andrew Rudd and Richard Grinold for their helpful comments.

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER 1988 E 73



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