**"modern portfolio theory"**

## Behavioral Portfolio Theory 1 – Safety First

*by Eric Bank on February 18, 2011 · No Comments · in Documenting the Search for Alpha*

ur 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).

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****μ**and return_{P}**standard deviation****σ**;_{P} - the
**risk-free asset R**is not available;_{F} - 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 – ****μ _{P}) / σ_{P}**

_{ }

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!

## Capital Asset Pricing Model, Part One – Normal Distribution

*by Eric Bank on January 7, 2011 · No Comments · in Documenting the Search for Alpha*

We are now ready to discuss asset pricing models, and we’ll begin with the Capital Asset Pricing Model (CAPM).

We left off last time showing how the **Security Characteristic Line** indicates the **beta** of an asset under Harry Markowitz’s **Modern Portfolio Theory (MPT)**. We are now ready to discuss asset pricing models, and we’ll begin by documenting the **Capital Asset Pricing Model (CAPM)**. This model was developed in the 1960’s by several independent researchers, including Sharpe, Treynor, Lintner and Mossin, building on Markowitz’s previous work.

CAPM is an equation that indicates the required **rate of return (ROR)** one should demand for holding a risky asset as part of a diversified portfolio, based on the asset’s beta. If CAPM indicates a rate of return that is different from that predicted using other criteria (such as P/E ratios or stock charts), then one should, in theory, buy or sell the asset depending on the relationship of the different estimates. For instance, if stock charting indicates that the ROR on Asset A should be 13% but CAPM estimates only a 9% ROR, one should sell or short the asset, which cumulatively should drive the price of Asset A down. Continue reading “Capital Asset Pricing Model, Part One – Normal Distribution” »

## Modern Portfolio Theory – Part Three

*by Eric Bank on January 5, 2011 · No Comments · in Documenting the Search for Alpha*

The Capital Market Line represents a portfolio containing some mixture of the Market Portfolio (MP) and the risk-free rate.

Our quest continues to find out whether hedge fund alpha really exists or is just hype. Recall from last time our documentation of the **Capital Market Line (CML)**. The CML represents a portfolio containing some mixture of the **Market Portfolio (MP)** and the **risk-free rate**. It is a* *special version of the **Capital Asset Line**, ranging from the risk-free rate tangentially to the **Efficient Frontier** at the Market Portfolio, and then extending upwards beyond the tangent point. **Modern Portfolio Theory (MPT)** posits that any point on the CML has superior risk/return attributes over any point on the Efficient Frontier. Let’s ponder that for a second – just adding some T-Bills to, say, S&P 500 baskets (our proxy for the Market Portfolio) will improve the risk/return characteristics of your portfolio.

If your entire portfolio consisted only of the cash-purchased Market Portfolio (i.e. the tangent point on the Efficient Frontier), your **leverage ratio** would be 1 – you are **unleveraged**. The points on the CML below the Market Portfolio represent **deleveraging**: adding cash to your portfolio. You are lowering risk and expected return when you deleverage. If you borrowed and sold TBills, and used the proceeds to buy additional Market Portfolio, your new portfolio would be **leveraged**, and would be a point on the CML above the tangent. Leveraging increases your risk and expected return. If you disregard the effects of borrowing (or margin) costs, then all points on the CML share the maximum **Sharpe Ratio**, a popular formula for expressing risk/return. Continue reading “Modern Portfolio Theory – Part Three” »

## Modern Portfolio Theory – Part One

*by Eric Bank on December 30, 2010 · No Comments · in Documenting the Search for Alpha*

Our risk/return series continues with a review of Modern Portfolio Theory (MPT). We’ve already looked at alpha, beta, efficient markets, and returns. Our ultimate goal is to evaluate the role of alpha in hedge fund profitability, how to replicate hedge fund results without needing alpha, and finally how you can start your own cutting-edge hedge fund using beta-only replication techniques.

Our risk/return series continues with a review of **Modern Portfolio Theory (MPT)**. We’ve already looked at **alpha, beta, efficient markets**, and **returns**. Our ultimate goal is to evaluate the role of alpha in hedge fund profitability, how to replicate hedge fund results without needing alpha, and finally how you can start your own cutting-edge hedge fund using **beta-only replication techniques**.

MPT suggests that a portfolio can be optimized in terms of risk and return by carefully mixing individual investments that have widely differing betas. Recall that beta is return due to correlation with an overall market (known as **systematic risk**). To take a trivial example, if you hold equal long and short positions in the S&P 500 index, your portfolio would have an overall beta of (.5 * 1 + .5 * -1) = 0. There would be no risk, but in this case, there would be no return either, except for the slow drain of commissions, fees, etc.

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