Several developments in Investment Theory have influenced how we specify and measure risk in the valuation process.

On this page, we will discuss the latest market consensus thoughts on efficient markets. Probably the most important innovation in recent years, Modern Portfolio Theory, will be laid out. Finally, we will talk about the latest thinking on asset pricing models.

*Perfect Markets*

*Perfect Markets*

We will begin this section with a description of the efficient market Hypothesis. Then, we will break it down in the various degrees of efficiency. The testing of EMH is then discussed. Finally, we will talk about how to use the results.

An **efficient capital market** is one in which asset prices adjust rapidly to the arrival of new info. Therefore, the current prices of assets reflect all info about the asset.

Efficient markets have been the most widely studied concept over the last four decades due its significance in the real world. At the same time, efficient markets have been the most controversial due to the wide variety of opinions.

*Efficient Market Hypothesis*

*Efficient Market Hypothesis*

###### Efficient Market Assumptions

- Large number of competing max profit players analyze and value assets
- New info about assets come to the market in random form
- Competing players attempt to adjust asset prices quickly to reflect the effect of new info
- Expected returns implicit in the current price of the asset should reflect its risk

The **random walk hypothesis**, forerunner of **Efficient Market Hypothesis** (EMH), contends random changes in stock prices. This stems from the unstructured and unpredictable way info is made known to players.

Unlike random walk which deals with prices over time, Eugene Fama’s (father of EMH) fair game model of EMH deals with price at a unique point in time.

*Alternate Forms*

*Alternate Forms*

Using facts, Fama further divided EMH into sub-hypotheses depending on their info set.

##### Weak-Form EMH

Assumes current stock prices fully reflect all market info including sequence of price, rates of return, trading volume data, and other market info. It implies past rates of return should have no tie with future rates. You have little to gain by making trading rules based on past market data.

##### Semistrong-Form EMH

Asserts prices adjust rapidly to the release of all public info. It includes the weak-form EMH but also includes all non-market info such as earnings/dividend announcements and economic/political news. It implies if you base your decisions on important info after it is made public, you will not derive above-average returns because the info is reflected in the price.

##### Strong-Form EMH

Contends prices fully reflect all info from public and private sources. No group has sole access to info relevant to its price. It includes both weak- and semistrong-forms. It assumes perfect markets where all info is cost-free and open to everyone at the same time.

**Testing and Results**

**Testing and Results**

##### Technical Analysis

Most of the testing of the weak-form suggest the trading rules generally would not outperform a buy-and-hold policy on a risk-adjusted basis after taking into account costs.The results support the weak-form hypothesis.

##### Earning Surprises

In order to test the semistrong form, you need to adjust for the market return to see if there is added return. The results show limited success in predicting short-horizon returns. However, the proof of long-horizon returns is quite solid.

The results suggest the info contained in quarterly earnings reports is not quickly reflected in stock prices. Therefore, a key bridge exists between the size of the earnings surprise and the post stock price change.

##### Calendar Studies

Calendar studies found **January effect** due to tax avoidance tactics. Investors tend to engage in tax selling at the end of the year to take losses on stocks that have declined. After the new year, they buy back these stocks or to buy others that look good.

Another study found a big monthly effect where all the market advance occurred during the first half of the trading month. In addition, French found over time the mean return for Monday was strongly down while all the other four days were up.

##### Cross-sectional Predictions

A number of quirks were found disproving the semistrong EMH form and offer areas to exploit. It found the returns for stocks in the lowest P/E quintile were better than those in the highest P/E quintiles.

The returns for long-term periods show small firms consistently receive higher returns than large firms. A closely related quirk occurs called the **Neglected Firm** effect where a lack of info and limited big firm interest yields higher returns.

In a famous study Fama and French found a big tie exists between book to market value and future stock returns. In addition, they found this tie persists when other factors were included.

##### Event Studies

Studies found stock splits do not result in higher rates of return after the split. Investors who are in an IPO get a quick positive return due to under-pricing but those who then buy in do not get higher returns.

Most studies point to higher returns when a stock applied for a national exchange listing but no long-term effects have been shown.

*Implications*

*Implications*

The result from fact testing EMH in its forms offers opportunities and areas to avoid.

##### Technical Analysis

A basic premise of this analysis is stock prices move in trends which persist. If the markets is weak-form, no trading system which depends only on past trading data should have any value.

##### Fundamental Analysis

This approach says there is a basic intrinsic value for the whole stock market, sectors or single stocks. An opportunity exists when the intrinsic value strays from its market value.

While you can’t make a prediction based on the past, you can get higher returns if you do a good job estimating future market data. If you can do a good job projecting earnings and your projections *differ from consensus*, you will have a good stock picking record.

Therefore, you should use the quirks such as size and book value ratios when picking a set of stocks or a single stock to analyze.

##### Portfolio Management

It is widely held the pros do not beat a buy-and-hold account on a risk-adjusted basis. Any success is due to access to great pickers.

If you have access to these great pickers, you should actively manage the account if you don’t have high costs. These pickers should focus their efforts in the mid-cap area where the market is less traded.

###### Managing Without Great Pickers

- Select and define risk profile
- Construct right risk level by splitting holdings between risk-free and risky assets
- Spread out on a global basis to cut unsystematic risk
- Maintain the right risk level by rebalancing when necessary
- Reduce taxes and total trading costs

*Portfolio Theory*

*Portfolio Theory*

One of the major advances in the field has been the notion an optimum portfolio is not simply a matter of mixing a lot of unique assets with good risk-return traits. You must consider the tie among the holdings.

In this section, we will describe MPT. WE will talk about how it is measured and how the optimal portfolios line up to form an efficient frontier.

**Assumptions**

**Assumptions**

###### Portfolio Theory Assumptions

- Investors want to maximize the returns from their investments for a given level of risk
- Investors are basically risk avers, meaning given a choice between assets with equal rates of return, the will select the asset with the lower level of risk
- Not everyone is risk averse

**Modern Portfolio Theory**

**Modern Portfolio Theory**

Harry Markowitz was the first to measure risk. He showed the variance of the rate of return was a meaningful measure of portfolio risk

###### Markowitz Model assumptions

- Investors consider each alternative represented by a probability distribution of expected returns
- They maximize one-period expected utility
- estimate risk on the portfolio of the basis of variability of expected returns
- base decisions solely on expected return and risk
- prefer higher returns to lower returns at a given risk level

A single asset or portfolio of assets is efficient if no other asset or holdings set offers higher returns with the same risk or lower risk with the same return.

##### Measures of Risk and Return

The best-known measure is the variance or standard deviations (SD) of expected returns. It is easy to understand, correct and widely used measure and it is found in many asset pricing models. Also, another measure of risk is the range of returns.

Co-variance of returns is a measure of the degree to which two factors move together. It involves direction and degree. This concept is speaking to the relation of assets in an account and points toward a measure of reducing risk.

**Efficient Frontier**

**Efficient Frontier**

The **efficient frontier** represents the set of holdings which have the max rate of return for every given level of risk or the min risk for every level of return.

Your choice for risk and return has its own range of limits are unique. Called your **utility curves**, not all will agree with your choices.

The *efficient frontier *is all the choices known. Therefore, where your utility function meets the efficient frontier lies your **optimal portfolio**. No other combo of risk and return will make you happier.

*Asset Pricing Models*

*Asset Pricing Models*

After Markowitz came up with MPT, two other major theories have been proposed to derive a model for the value of risky assets. In this section, we will discuss assumptions for the them, describe their models and go over the testing.

In this section we will apply some MPT principles to pricing individual assets with CAPM. Then we will discuss an alternate theory, APT. Finally, we will talk about the testing of the theories.

**Capital Market Theory**

**Capital Market Theory**

This theory extends MPT and comes up with a model for pricing all risky assets. The final product, the **Capital Asset Pricing Model (CAPM)** will allow you to find the required rate of return for any risk asset.

###### Assumptions of Capital Market Theory

- Your optimal portfolio depends on your unique risk–return set
- You can borrow or lend any amount of money at the risk-free rate (RFR)
- Investors have the same thoughts about the future
- Investors have the same one period time set
- All assets are finitely divisible
- No taxes or trading costs
- No inflation or any change in rates
- Markets are in equilibrium

Some of theses factors may seem bogus. Easing many of them would only have a minor bump. The theory shouldn’t be judged on its assumptions but on how well it explains and helps us predict the real world.

The anchor of CAPM is the risk-free rate which as zero tie with all other risky assets. In real life, the risk-free asset is the US Treasury with a term covering the time we are studying.

Grouping all risky assets gives us the set of possible assets or the **market portfolio**. This spread out set has no unsystematic risk because all the risk unique to single assets are diversified away.

Only systematic risk, measured in SD, remains. It can change over time as macro factors such as growth in the money supply or production changes.

The combo of risk and return of the market portfolio with no unsystematic risk forms the *capital market line*. Investors should only differ where they want to be by their **financing decisions**. If you’re risk averse, you will lend some part of your holdings by buying the risk free asset.

CAPM states the expected or required rates of return on risk assets. Beta is a fixed measure of systematic risk. It relates to the relative variance of an asset to the market. Therefore, the riskier the asset, the more you will want to be paid for holding it.

An analyst estimates the expected return of the asset. If the expected return exceeds its *risk premium* plus the risk-free rate, then she suggests a buy. If the expected return doesn’t cover the risk premium plus RFR, then the asset should be skipped.

**Arbitrage Pricing Theory**

**Arbitrage Pricing Theory**

One of the drawbacks of CAPM is that beta is not stable over time. Other downsides include lack of access to the market portfolio and coming up with a means of track record measure is not useful. The **arbitrage pricing theory** (APT) is easy to grasp and has few factors.

###### APT Assumptions

- Markets are perfect
- Investor always prefer more wealth to less wealth with no risk
- The stochastic process giving asset returns is a factor model

A *stochastic* event or system is one which is not certain because of a random factor. In probability theory, a *stochastic process* is a time sequence showing the movement of some system marked by a factor whose change is subject to a random act.

APT contends many factors have an impact on the returns of all assets. CAPM contends the only key factor is beta.

The APT model spits out its expected returns. If the prices of the assets do not reflect these returns, we would expect investors bargain. Thus, they would sell overpriced assets short and use the proceeds to buy the cheap asset until the prices are correct.

**Empirical Testing**

**Empirical Testing**

Many tests found conflicting results. APT was able to explain other rates of return with better results to CAPM. On the other hand the model could not explain the small firm effect nor find the many factors behind the results.

APT is somewhat new and needs more testing. Its worth the effort due to being simple.

On this page, we will discussed the latest market consensus thoughts on efficient markets. Probably the most important innovation in recent years, Modern Portfolio Theory, was laid out. Finally, we will talked about the latest thinking on asset pricing models.