Posts by author: Eric Bank

Our survey of hedge fund strategies continues. Intermediate between long/short equity hedging and equity hedged market neutral is a fairly recent innovation: enhanced active 100X –X (EA). As briefly mentioned last time, an EA portfolio has the following characteristics:

  • Contains short positions equal to some percentage of the book (X, generally 20 percent or 30 percent but possibly more) and an equal percentage (100 + X) of leveraged long positions.
  • Relies on prime brokerage structures, include security lending, that allow short proceeds to purchase long positions without additional margin.
  • Makes use of quantitative techniques to actively manage selection, timing, and hedging ratios.

For example, a hedge fund manager allocates a percentage of his/her capital, say 30%, to short positions, and then uses the proceeds from the short sales to put on a long position equaling 100% plus the amount shorted – in this case giving a total long position of 130%.  This example would be called an enhanced active 130-30 strategy.   Note that the offsetting long and short positions leaves the portfolio with the same beta it would have with just a 100% long investment, but with a measure of downside protection not available in the long-only strategy.  Theoretically then, if the fund manager can differentiate strong and weak stocks, the 130-30 portfolio should outperform its 100-0 counterpart due to equal upside potential but decreased downside risk.

When a fund manager is competing against a benchmark, the enhanced active strategy provides greater flexibility to underweight weak stock and overweight strong stocks compared to long-only strategies. This is because the EA fund manager can achieve through shorting an underweight less than zero, which is the minimum weight in a long-only strategy. There is evidence that a stock is more likely to be overvalued rather than undervalued; hence underweighting should be more valuable than overweighting, and since underweighting is easier using an EA strategy as compared to using a long-only one, EA should have better returns (i.e. less risk).

Note that, given appropriate leverage flexibility, an EA 200-100 strategy would have $3 (300%) invested for each $1 (100%) of capital. This differs, however from the more traditional equity hedged market neutral strategy, which would invest equal amounts (3 x 100%) in long, short, and benchmark positions. That’s because the 100% invested in the benchmark, although providing market beta, is inflexible, and hence a potential drag on return. In contrast, the EA 200-100 has complete flexibility in portfolio selection, and thus affords fund managers an opportunity to “strut their alpha” (assuming they have any). Parenthetically, since the EA strategy uses short proceeds for additional leverage, it does not trigger Unrelated Business Taxable Income (UBTI) tax liabilities; in contrast, using margin to increase leverage will engender UBTI taxes.

Normally, SEC Regulation T prohibits leverage to 150% of capital, but through security-lending techniques available from prime brokers, this problem can be sidestepped. Prime brokers also facilitate EA strategies by allowing long positions to satisfy the maintenance margin requirements for short positions – no additional cash or security collateral is needed. Instead, the broker will charge a stock loan fee to cover its costs.  Dividends received will normally exceed dividends owed, so ultimately there is little need to tie up cash with an EA strategy.

One risk encountered in any long/short portfolio but absent from a long-only one is unlimited upside on a shorted stock.  A long position can only go to zero if a stock tanks; there is no limit on the loss caused by a short position on a skyrocketing stock unless the portfolio is actively managed and balanced. Because short positions have this additional risk factor, long/short portfolios should have access to a systematic (beta) risk premium, and hence greater average returns, than their long-only brethren. Of course, this additional risk is somewhat offset by decreased downside risk on long positions. The net effect is situationally-dependent.

Commissions are typically higher in EA portfolios relative to long-only ones, due to higher balancing activity in the former.  The ultimate test of an EA strategy, and its manager, is whether it nets, after fees and commissions, an alpha return (above-market return on a risk-adjusted basis), and does it do so year-in, year-out. We view this with a skeptical eye, and will continue that viewpoint as we next move our discussion to hedged market neutral strategies.

 

A long/short equity hedging strategy consists of selecting a core long equity portfolio and then partially or fully offsetting it with short equity positions. The goal is garner returns that resemble those available from a long call option – upside exposure and downside protection. The short equity positions may take the form of short stock positions, short call/long put options, and short futures/forwards, among others.

Most practitioners of long/short equity hedging tend towards a directional long bias – they do not completely hedge their long positions. Of course, in difficult market conditions, this bias may disappear or be reversed. Different styles of investing (such as ones based upon geography, sector, capitalization, book value, etc.) can overlay this strategy. So, for instance, a long/short portfolio may be long “undervalued” stocks or stocks from neglected countries or sectors, and short “overvalued” stocks from popular regions or sectors. Of course, notions of valuation are in the eyes of a fund manager, but there is a general consensus that, for instance, small-cap stocks are systematically undervalued, and hence provide a risk premium (in the case of small-cap stocks, the risk premium is often called a liquidity premium), relative to large-cap stocks. Another example of systematic risk premia involves so-called “value” stocks, as opposed to “growth” stocks. Thus, a typical long/short portfolio may be long small-cap and/or value stocks, and short large-cap/growth stocks (or equivalent short positions in indexes or derivative instruments).

There are many other ways to target undervalued stocks using fundamental analysis in either a top-down or bottom-up approach. Top-down analysis involves identifying socio-economic trends, and then sectors and companies that will benefit therefrom. Bottom-up stock selection rests on the information gleamed from a company’s financial statements, SEC filings, and various external reports (research reports, news articles, personal interviews, trade shows, etc.). In either approach, fund managers may be free to put on positions as they see fit – there need not be any benchmark portfolios associated with a long/short strategy. Thus, managers using this strategy can be unencumbered with the potential drag of trying to outperform a benchmark portfolio.

So, how much does a manager’s superior skill (alpha) contribute to returns from a long/short hedge fund? We have seen that built-in systematic risk premia (beta) can be a significant source of return, as in small-cap or value-based positions. Studies have indicated that up to 70% of returns from this strategy are a result of market exposure. The fact that the strategy works much better in strong up-markets than in flat or bear markets reinforces the perception that much of the return reaped by hedge funds utilizing a long/short strategy arises from beta, and that the added kick provided by alpha may be over-hyped.

A recently-popular variation on the long/short strategy is known as the “enhanced active 100X –X” strategy. A hedge fund manager allocates a percentage of his/her book, say 30%, to short positions, and then, through the use of prime brokerage leverage techniques uniquely available to hedge funds, uses the proceeds from the short sales to put on a long position equaling 100% plus the amount shorted – in this case giving a total long position of 130%. This example would be called an active 130-30 strategy. Quantitative techniques are often used in this variation; as such, it might be termed a hybrid of long/short equity hedging and equity hedged market neutral investing. Before we turn to the latter strategy, we’ll continue next time with an in-depth review of enhanced active 100X-X investing.

Consumption Risk?

When we recently examined Intertemporal Capital Asset Pricing Model (I-CAPM), we understood it to be an extension of CAPM in which investors establish additional portfolios to hedge specific risks representing short-term idiosyncratic tastes and preferences. Typical examples of these specific risks include inflation, job loss, economic downturn, etc. The model is somewhat incomplete, in that it doesn’t specify how to arrive at the proper factors to quantify these additional hedges.  Another approach, called the Consumption CAPM (C-CAPM) posits a single additional hedge portfolio based on consumption risk, which is a hedge against future consumption rates.  Let’s see how that works.

C-CAPM assumes that investors are not interested in maximizing their portfolio, but rather in maximizing over their lifetimes the consumption they get from their portfolio.  Therefore, there is a tradeoff between current and future consumption. The model assumes that investors will sell assets during bad economic times and buy them when times are good. That means that, say, a yacht, will have to have a very high future expected return (a high risk premium) to induce the owner to hold onto it when times are bad. Therefore the systematic risk of the asset (the yacht) is tied to the state of the economy.

An illustration will clarify.

Each person has their own set of utility functions. For instance, if I buy an asset (such as a yacht) today, it will cost me $X.    If I am to hold off on buying the asset, it had better be worth it to me to wait.  In other words, I should receive a return on the amount, $X, that I didn’t consume today.  If that return, which we’ll call the consumption premium, is high enough, I’ll wait; if not, I’ll buy the asset today. At some rate of return (let’s call it r0) I am indifferent to waiting or consuming. If my return on $X is expected to exceed r0, I’ll wait. If it is expected to be less than r0, I’ll consume today.

Now, if I expect a rosy economic future, I will assign a higher risk premium to the yacht; conversely, if I see the future economy tanking, I lower risk premium on the yacht, making it more likely to consume the asset now rather than waiting.  Of course, if I’m anticipating a severe depression, I just might keep the $X in Treasury bonds and adjust my utility function accordingly.  Since the price of my current Treasury bonds will rise during a depression (because of their relatively high interest rates), they are a good hedge against bad times – something that cannot be said about a yacht. In terms of C-CAPM theory, the returns on the Treasury bonds have a negative correlation with consumption, and are thus are worth more during times of depressed consumption. The yacht’s returns have a positive correlation with consumption (yachts sell for more in times of consumption growth), and are therefore worth less during low-consumption periods.

Bottom line: hedge your portfolio with assets that will do well when economic consumption rates drop.

In C-CAPM, one has to measure the consumption premium accurately in order to have a valuable model. One problem that arises is that of satisfice:  are consumers really looking to optimize consumption, or are they merely satisfied with achieving some minimum constraint? This will have considerable impact on the rate at which future consumption is discounted to arrive at its value today.

Now that we’ve looked at CAPM and several alternatives, we want to next explore the topic of specific risk premia, which we’ll loosely define as the return (above the risk-free rate) that can be associated with taking on certain systematic risks.  We want to see whether, for any given hedge fund strategy, returns can be ascribed solely to the systematic risks (i.e. beta) of the strategy, or whether some portion of the return is due to a superior fund manager (alpha).  This will lead to our ultimate topic: hedge fund replication.

In earlier blogs, we explored how prime brokers lend securities.  Today we’ll take a closer look at the U. S. regulations that control security lending.

Regulation T

Under the Federal Reserve’s Regulation T, a security can be loaned at a minimum of 100% of its value for a permissible purpose.  The purposes are to cover shorts, assure settlements or to loan to another. It also details the allowable collateral for such trades. The regulation states:

“Without regard to the other provisions of this part, a creditor may borrow or lend securities for the purpose of making delivery of the securities in the case of short sales, failure to receive securities required to be delivered, or other similar situations.  Each borrowing shall be secured by a deposit of one or more of the following: cash, securities issued or guaranteed by the United States or its agencies, negotiable bank certificates of deposit and banker’s acceptances issue by banking institutions in the United States and payable in the United States, or irrevocable letters of credit issued by a bank insured by the Federal Deposit Insurance Corporation or a foreign bank that has filed an agreement with the Board on Form FR T-2.  Such deposit made with the lender of the securities shall have at all times a value at least equal to 100 percent of the market value of the securities borrowed, computed as of the close of the preceding business day.”

While the required margin is 100%, the standard collateral margin required per the Stock Loan Agreements is 102% for U.S. securities and 105% for non-US securities.  This is the determined hedge required against market exposure due the market value being computed as of the preceding business day.  Also, while in addition to cash collateral, the regulation allows for Letters of Credit, Certificates of Deposits, or securities as collateral on loans. The SEC will now allow, in addition to the US Treasury bills and notes, any obligations issued by the any agency or instrument of the U.S. including FNMA, FHLMC and certain other securities which are not backed by the full faith and credit of the U.S. government.  Zero Coupon Bonds and Strips are not allowable collateral pursuant to this rule.  The Fed does not object to cash collateral in the form of foreign currency if the currency is that of the security’s country of issuance.  However, this is all at the discretion of the lenders, thus, allowable collateral is stated in the Loan Agreement.

Rule 15c3-3

This is a Security Exchange Commission (‘SEC’) Rule.  The rule is applicable to registered broker dealers trading on behalf of customers.   Audit confirmations from any brokers trading for customer accounts may be received with wording to the effect of “In accordance with Rule 15c3-3, please confirm the following loans to us”.   Additionally, some of the requirements of this agreement correspond to some points made in the Securities Lending Agreement and may shed some light on the relevance.

This is part of the Customer Protection Rules of the Securities Exchange Act of 1934 and details provisions of the written Securities Lending Agreement. The written agreement must at a minimum meet the following requirements:

  1. In a separate schedule, include basis of compensation for any loan and the rights and liabilities of the parties as to the borrowed securities.
  2. Provide that the lender will receive a schedule of securities actually borrowed at the time of the borrowing of the securities.
  3. Specify that the broker/dealer:
  • Provide collateral consisting exclusively of cash, US Treasury bills or notes or irrevocable letters of credit issued by a bank as defined in Section 3-(a) (6) (A)-(C) of the Securities Exchange Act, which fully secures the loan of securities.  Notice that Regulation T expands on the list of allowable collateral.
  • Must mark the loan to market daily. In the event that the market value of all outstanding securities loaned at the close of business exceeds 100% of the collateral held by the lender; the borrowing broker must provide additional collateral as described above to the lender by the end of the next business day.  At the end of the day the total collateral held by the lender cannot be less than 100% of the market value of the loaned securities.
  • Post a prominent notice that the provisions of the Securities Investor Protection Act of 1970 may not protect the lender with respect to the securities loan transaction.  This means that the collateral held by the lender of the loaned securities may be their only source of satisfaction of obligation by the borrower if the borrower fails to return the securities loaned.
Picture of Einstein writing on blackboard

He would understand I-CAPM.

The Capital Asset Pricing Model (CAPM), which estimates the return on an asset by its co-varying relationship (its beta) with the market portfolio, has spawned a whole field of study devoted to improving upon the original model.  We have already explored D-CAPM, which modified beta to measure downside risk rather than total risk.  Our attention now turns to another alternative theory, the Intertemporal CAPM (I-CAPM). As in previous discussions, we omit the complicated mathematics.

I-CAPM was first introduced in 1973 by Merton. It is an extension of CAPM which recognizes not only the familiar time-independent CAPM beta relationship, but also additional factors that change over time (hence “intertemporal”).  Specifically, Merton posited that investors are looking to hedge risks based on current and projected factors, such as changes in inflation, employment opportunities, future stock market returns, etc. Thus, an I-CAPM portfolio contains a core investment tied to the market portfolio, plus one or more hedge portfolios that mitigate an investor’s currently-perceived risks. Since each investor has his/her own perceptions of risk, I-CAPM is hard to generalize to a population of investors. Also, the correct factor to use for any given hedge is ambiguous: if you think you might be unemployed 3 years from now, which factor do you choose to hedge?

So, I-CAPM is a multi-factor model that attempts to capture more determinants of risk than just beta, but does not provide concrete guidance for identifying which additional factors to use, or even how many of them to include.

A popular “fix” to this problem has been to employ the Fama-French Three-Factor Model (FF), which states that the two additional factors beyond beta should be used to improve CAPM.  These two factors relate to specific investment styles:

  • Liquidity: small capitalization stocks outperform large-cap stocks
  • Value: value stocks outperform growth stocks

FF speculates that these two stock groupings, small cap and value stocks, are inherently more risky to macroeconomic downturns and thus are required by investors to provide higher returns (hence portfolios built on these factors should have betas higher than 1.0, the market beta). However, FF posits that the risk premia provided by these two factors exceeds that provided by a higher beta alone – that there is an alpha component (representing non-systematic risk) to the returns generated by portfolios built on these factors. But I-CAPM requires efficient markets, which would mean that each factor’s risk premium is due only to its beta. Hence, I-CAPM argues against alpha-based returns, which indeed is the overall conclusion we have been seeking to evaluate over the past months.  We will keep returning to this question, as it has serious implications for our ultimate topic: alternative beta strategies and hedge fund replication.

Payment date calendar

Payment date calendar

Many trading firms, especially ones that are not self-clearing, use prime brokerages to maintain accounting books and records on the trading firm’s behalf. Accrual accounting is used: items are recognized when they are earned and expenses recognized when they are incurred.

Because accrued-based accounting is used, in some cases accruals are set up in the the General Ledger to record income or expenses that have been earned but not received.  The two most common are dividends and coupon interest, and what follows is a typical scenario followed by a prime broker to handle these two items. First, a few important dates are defined:

  • Record date: whoever owns the securities on the close of the record date is entitled to the dividend
  • Ex-dividend date: first trading date following the record date; dividends are not due to security holders as of this date. Also known as the ex-date.
  • Trade date: date on which a trade occurs
  • Settle date: date on which a trade is settled – on that date, cash and securities are exchanged.
  • Pay date: date on which a dividend or coupon are paid. For interest, also known as the coupon date.

Dividends

Dividends are booked using the ex-dividend date as the trade date and pay date as the settle date. The broker’s Dividend Accrual Report shows the trading firm’s dividends posted for common stock in which the dividend transactions are past the ex-date (i.e., trade date) but have not yet reached the pay date (i.e., settle date). This is usually no more than a 3-day gap domestically. Accountants create accrual entries for the General Ledger during month-end closing cycle based upon the Dividend Accrual Report.

Coupon Interest

Coupon interest is booked on the coupon date (trade date = settle date = coupon date). Accrued interest is not booked in the firm’s transaction database except upon the purchase or sale of an interest-bearing instrument. Interest accrued between the time of a bond purchase and the next coupon date is not recognized in the transaction database until realized on the coupon date (or upon closing of the bond position), but must be accrued monthly in the General Ledger. Therefore, the accountants run an Interest Accrual Report at month-end that shows the accrued interest earned within the month. They create accrual entries for the General Ledger during month-end closing cycle based upon the Interest Accrual Report.

Because the cash from the coupon payment is paid on the coupon date, the coupon’s effect on the trading firm’s cash balances on that date are available for use by cash managers.

Firms usually also receive a Consolidated Accrual Report that reports all accruals for the month, not just dividend and interest.  These include income and expense entries reflected in the company’s receivables and payables.

Ocean lIner sinking at severe angleWe have devoted a lot of blog space in the past examining the pros and cons of the Capital Asset Pricing Model (CAPM).  The model predicts the amount of excess return (return above the risk-free rate) of an arbitrary portfolio that can be ascribed to a relationship (called beta[1]) to the excess returns on the underlying market portfolio. It assumes that investors seek maximum utility from their portfolios, and that investors expect to be compensated for taking on additional risk. In CAPM, no portfolio can outperform a mix of the risk-free asset and the market portfolio on a risk-adjusted basis.

Risk and return are the only two variables of importance in CAPM.  Risk is measured by beta, which is rooted in the variance (or more properly, its square root, standard deviation) of returns, and is an indication of volatility.

Recall that CAPM makes a number of simplifying (and criticized) assumptions to work.  A couple of the assumptions that have been the subject to criticism are:

1)     Portfolio returns are distributed symmetrically around a mean.

2)     Portfolio returns are assumed to have no outliers (or “fat tails”).

Empirical evidence suggests otherwise. Researchers have thus sought alternatives to a variance-based beta that relaxes both of these assumptions, and one popular candidate is called semivariance – a measure of the dispersion of those values in a distribution that fall below the mean or target value of a data set. In short, semivariance-based modifications to CAPM concentrate on downside-risk only. Semivariance is a better statistic when dealing with asymmetric distributions, as it automatically incorporates the notion of skewness. Ignoring skewness, by assuming that variables are symmetrically distributed when they are not, will cause any model to understate the risk of variables with high skewness

One popular semivariant CAPM alternative is called D-CAPM (Downside-CAPM).  Regular old beta is replaced by downside-beta (βD). Different researchers have supplied different technical definitions for βD; here we will use the one provided by Javier Estrada:

βD = downside covariance between asset and market portfolio / downside variance of market portfolio.

There are several ways to calculate βD, but I will spare you the details. The important point is that empirical studies[2] indicate D-CAPM gives better predictions compared to CAPM, especially for emerging markets.  This may be due to the hypothesis that returns from emerging markets are less normal and more skewed than returns from developed markets.

D-CAPM is generally well-regarded because of its plausibility, supporting evidence, and the widespread use of D-CAPM.  For instance, a study by Mamoghli and Daboussi[3] concluded “It comes out from these results that the D-CAPM makes it possible to overcome the drawbacks of the traditional CAPM concerning the asymmetrical nature of returns and the risk perception…

However, D-CAPM is not without its critics.  Let me quote from one[4], in which downside correlation is taken to task: “This measure ignores the ability of upside returns of one asset to hedge the downside returns of another asset in a portfolio. Within the scope of D-CAPM the standard equation to calculate portfolio’s downside semideviation cannot be correct, since the Estrada’s downside correlation equates upside returns to zeros and does not represent the true downside correlations. Specifically, the downside correlation cannot be measured, because the portfolio’s semideviation depends on the weights of assets, their standard deviations and correlation between them, rather than on the semivariance. This formula is specified for normally distributed and symmetrical returns and there is no formula invented to calculate the portfolio’s semideviation yet”.

This criticism, if true, is especially relevant to hedge fund traders, who use long-short strategies as a matter of course.

Nevertheless, Professor Estrada responded[5] as follows: First, it’s true that the downside beta I suggest in my paper does not account for something that would be legitimately called risk, which is the market going up and the asset going down. The way I suggest to calculate downside beta only accounts for down-down states. But there is a reason for this: It’s the only way to achieve a symmetric semivariance-semicovariance matrix, necessary for a solution of the problem. For example, the only way to apply standard techniques to solve an optimization problem with downside risk is to have a symmetric matrix. Second, and importantly, my several papers on downside beta, D-CAPM, and downside risk in general have been published in several journals and therefore peer-reviewed. I believe Mr. Cheremushkin’s comment is an unpublished piece.”

This controversy will no doubt be resolved over the fullness of time. We welcome your views.


[1] Technically, beta is equal to the covariance of an asset with the market portfolio divided by the variance of the market portfolio.

[2] Estrada, Javier (2003). “Mean-Semivariance Behavior (II): The D-CAPM.”  University of Navarra.

[3] Mamoghli, Chokri and Daboussi, Sami (2008). Valuation of Hedge Funds Portfolios in a Downside Risk Framework.

[4] Cheremushkin, Sergei V. (2009). “Why D-CAPM is a big mistake? The incorrectness of the cosemivariance statistics.”  Mordovian State University.  Also private communication 9-Aug-10.

[5] Private communication 9-Aug-10.

Last time we began our discussion of Behavioral Portfolio Theory with a look at Safety-First Portfolio Theory (SFPT), which basically posits investor motivation to be to avoid ruin.  An extension to SFPT was introduced in 1987 by Lopes, named SP/A Theory. The letters in its title can be summarized:

S = security, a general concern about avoiding low levels of wealth

P = potential, reflects the general desire to maximize wealth

A = aspiration, the desire to reach a specific goal, such as achieving no less than the subsistence level s.

SFPT is a psychological theory of choice under uncertainty. In Lopes’ framework, risk-taking is balanced between fear and hope. Lopes posits that fear is such a strong factor because fearful people overweight the probability of the worst outcomes, underweight those for the best outcomes. This leads individuals to understate the probability of achieving the highest level of expected wealth E(W).  In other words, fearful individuals are pessimistic.

Hope has the inverse effect on individuals – optimism causes hopeful investors to overstate the probability of achieving the highest level of expected wealth.

For those of you who like symbols, wealth W is actually a series of n different levels of wealth, ordered from lowest to highest, designated as W1, W2, W3, … Wn-1, Wn. Lopes denotes a decumulative distribution function[1] D(x) as the likelihood that the wealth W of a portfolio will be greater than the investor’s subsistence level s:

D(x) = Prob {W >= s)

where 0 < x <= n different levels of wealth.

Expected wealth E(W) is the weighted sum of each level of wealth, the weight being the probability pi of achieving a particular level of wealth Wi:

E(W) = ∑piWi

Lopes notes that expected wealth, E(W) = ∑piWi, can be expressed as the sum of the decumulative probabilities ∑Di (Wi - Wi -1), where the summation is from i = 1 to n and W0 is zero. In this expression for E(W),the individual receives W1 with certainty (note that decumulative probability D1 = 1), receives the increment W2 – W1 (that is, an amount over W1) with probability D2, receives the further increment W3 – W2 with probability D3, and so on. Lopes contends that fear operates through an overweighting of the probabilities attached to the worst outcomes (W1). The way that works is that fearful investors set the p1 too high, and pn too low. The reverse is true for hopeful investors.

Lopes concludes that the emotions of fear and hope reside within all individuals, and that each emotion serves to modify the decumulative weighting function D. She suggests that the final shape of the decumulative transformation function h is a convex combination (shaped like a smile) of hs (for fearful investors worried about security) and hp (for hopeful investors looking for maximum potential), reflecting the relative strength of each.

The qualitative lesson from SP/A theory is that you should establish a portfolio in which you have reigned in your emotions of fear and hope, so that neither dominates. Unfortunately, it doesn’t tell you how to accomplish this. Still, not a bad lesson for a hedge fund trader.


[1] The decumulative distribution function is just (1 – cumulative distribution function).  Basically it measures the curve to the right (instead of the left) of a given point.

Man working belt and suspenders

Safty First!

Our survey of portfolio theories continues; we have already evaluated Modern Portfolio Theory, the Capital Asset Pricing Model and the Arbitrage Pricing Theory in earlier blogs, and now turn to a series of articles on Behavioral Portfolio Theory (BPT).  Recall that as we continue to lay out a financial framework, our ultimate goal is to figure out whether hedge funds actually provide alpha returns to investors.

Whereas both CAPM and ABT assume that investors are proceeding from a single unified motivation – to maximize the values of their portfolios – BPT instead suggests that investors have a variety of motivations and structure their investments accordingly.  Think of a layered pyramid, in which the base is set up to protect against losses and the top designed for high reward.  This has been characterized as the “government bond and lottery ticket” portfolio because of the extreme divergence of goals.

One of the earliest attempts at BPT was Safety-First Portfolio Theory (SFPT, Roy 1952). The theory posits that investors want to minimize the probability of ruin, which is defined as when an investor’s wealth W falls below his subsistence level s:

min Pr(W < s).

SFPT, like the other portfolio theories, makes a few assumptions:

  • a portfolio has a return mean μP and return standard deviation σP;
  • the risk-free asset RF is not available;
  • investors trade off assets according to the expected utility of the assets and the law of diminishing returns;
  • the subsistence level s is low; and
  • the distribution of portfolio returns is normal (bell-shaped).

In short, an investor wants to own a portfolio for which

(s – μP) / σP

is minimized.

Later refinements of the theory included:

  • relaxing the fixed value s;
  • constraining the probability of ruin such that it never exceeds a predetermined ruin probability
  • expecting investors to maximize wealth within the safety-first constraint

As an early behavioral portfolio theory, SFPT has a somewhat simplified vision of investor as primarily risk-adverse. Also, it postulates that investors follow utility theory in their decision-making, an assumption widely discredited by empirical studies.

We progress next time to a theory that had its roots in SFPT: SP/A Theory, which deals with security, potential, and aspiration. Don’t miss it!

New York Stock Exchange

Having previously discussed them, let’s compare them. How does the Arbitrage Pricing Theory (APT) stack up against the Capital Asset Pricing Model (CAPM)?

Both theories are important mechanisms for pricing assets.  The APT assumes less than CAPM. Whereas CAPM relies on probabilities and statistics, APT provides for cause and effect to explain its predictions of asset returns.  CAPM assumes investors hold a mix of cash and the market portfolio, whereas APT allows each investor to hold his own portfolio with its own unique beta. So if you applied APT to the market portfolio, the example would degenerate into CAPM, because the securities market line would be a single factor price model in which beta is exposure to price changes in the market portfolio.

Since the beta in CAPM is correlated to asset demand based on each investors incremental utility for each asset, it is considered a demand-side model. In contrast, APT is a supply-side model, because its betas correlate an asset’s return to specific economic factors.  Any sudden change to one of these factors would ripple through the market containing the asset, and thus are inputs to asset returns.

Both models assume perfect competition within markets:

  • Buyers are price-takers, and are too small to affect prices.
  • Assets are infinitely liquid, and  supply and demand will reach equilibrium at a certain price.
  • There are no barriers to entering or leaving a market.
  • There are no trading costs such as commissions, taxes or fees.
  • All investors share a sole motivation: to maximize returns.
  • A given share of a security is the same as any other share, regardless of where (i.e. on which exchange) the security is exchanged.

The only factor in CAPM is the market portfolio. ABT is a multi-factor model and has one additional requirement: the number of factors must be no greater than the number of assets.  Certain assumptions are made about APT factors:

  • The factors are macroeconomic in nature, and thus create risks that cannot be easily avoided through diversification.
  • Factors affect asset prices through shocks (unexpected changes).
  • All information about each factor is well-known and accurate.
  • There is some real-world relationship between a factor and an asset.

So, which model better predicts asset returns? The answer is not clear. Quoting from a study published in the Asia-Pacific Business Review, March, 2008 by Rohini Singh: “The macroeconomic factors used in this study were able to explain returns marginally better [using APT] than [CAPM] beta alone. While this confirms that risk is multidimensional and that we should not depend on beta alone, further research is required to identify other variables that can help explain the cross section of returns.