Investor Behaviour and Capital Market efficieny

Alpha (a) = E[R]s - Rs

WHY DO INVESTORS HOLD INEFFICIENT PORTFOLIOS?

Trading on News or Recommendation

Takeover Offers
Takeover bids are offers by a company to buy the shares of another company. This raises the share price of the company being bid for, as the shares will be purchased at a premium. Investors could profit of this information, if they knew for certain which bids would be successful as companies that have been taken over earn abnormal gains over time.

Recommendations
When investors who have an overconfidence-bias invest in the shares that have been recommended by expert authorities with no accompanying news, the share price rises rapidly and later falls over time below the market. Investors could obtain abnormal gains by shorting these stocks while the price is high.

The Performance of Fund Managers
Talented mutual fund managers, while able to generate more gains than the market average, do not bring superior value to individual investors. This is because the excess gain over the market, will be captured by the mutual charge fees.

Using Factor Portfolios
A collection of well-diversified portfolios to bring about ONE efficient portfolio. These factor portfolios' risk and return is altogether estimated through a formula known as the Multifactor Model of Risk. This model requires taking the sum E(Ri)= rf + βi [E(Rf ) – rf] of each of the factor portfolios. With the help of this model, we are able to cover all systematic risk for the efficient portfolio.

Selecting the Portfolios
The first portfolio should consist of a long position in the market portfolio and be financed by a short position in a risk-free security.The remaining portfolios should use the trading strategies of market capitalization, book-to-market ratios, and past returns as they tend to produce high positive alphas.This means they capture risk not covered by the market portfolio.

Excess Return of the Market

-Market Portfolio is used first because it covers a lot of systematic risk even when inefficiend and tends to have large premiums over short-term risk-free investments such as low risk money market funds and treasury bills because they have short maturities. Risk-free assets are ones with certain returns.
-This is what makes it the best portfoilio to use as a starting point in the multifactor model when identify collections containing the efficient portfolio.
-Given by: Mkt -rf

Market Capitalization Strategy

A technique in which risk is adjusted is simply by organizing a collective set of firms with market values below the median of the NYSE firms' equally weighted portfolio and those firms above the median. Through the buying and short selling bits of the small firms' stocks, the big stocks are purchased. This self financing technique proves to be a very effective strategy. This is also known as the 'Small-minus-Big' portfolio (SMB)

Fama-French-Carhart Specification

The compilation of the above four portfolios into one formula to derive the not only the collective expected return, but also the sensitivity of the stock to each portfolio. The formula is stated as follows:E(Rs)= rf + βmkt [E(R mkt ) – rf] + E(ri)= rf + βsmb [E(R smb ) – rf] + E(ri)= rf + βhml [E(Rhml ) – rf] + E(ri)= rf + βpr1yr [E(R pr1yr ) – rf]

Book-to-Market Ratio Strategy

Another risk adjustment technique is through analyzing book-to-market ratios of selected stocks of various firms. Those with ratios less than the 30th percentile of the NYSE firms' equally weighted portfolio are taken into account as the low portfolio and the ones with ratios higher than the 70th percentile are considered the high portfolio. With the use of a long position of low portfolios and their short sales enables to ability to buy high portfolios. This self-financing portfolio is known as the high-minus-low portfolio. (HML)

Past Returns Strategy

A second name for this strategy would be the 'Prior one-year momentum' portfolio. (PR1YR) It's an assortment of stock returns of the past year, and requires taking into account the portfolios which ranks top 30% and those, ranking bottom 30% and holding them for one year.

Rational Expections

attributes to investors interpreting their own collated information being a CAPM assumption

If a significant number of investors do not operate on rational expectation and carefree of other aspects of their portfolios besides E[R] & Volatility, the market portfolio will be INEFFICIENT.

Homogeneous Expectations

attribute similar expectations in all investors resulting from acquisition of same stock information.

An increase in the price of a stock will result in a zero alpha [a] & restore equilibrium as in the example.

Why do they occur?

(i)DISPOSITION EFFECT: Investors hold on to stocks that have depreciated and sell stocks that have appreciated.

(ii)Most traders are part-time traders and are affected by:

(iii) Investors blinding follow eachothers behaviours: HERD BEHAVIOUR

MOMENTUM

The momentum strategy has been tried and tested for decades and is based purely on historical data.
Stocks with high returns in the past have a tendency to continue with positive alphas.
However, CAPM theory states that if a market if efficient, the past returns would not be able to predict alphas.

SIZE EFFECT

Excess Return and Market Capitalisation
Stocks were divided into several portfolios based on size, and their monthly excess returns were plotted on a graph, the ones with higher Beta (smaller capitalisation) tend to be above the SML, but the smallest stock (highest risk) has the highest alpha.

Excess Return and book-to-market ratio
Value stocks (high book-to-market ratio) tend to be above the SML with positive alphas, and growth stocks tend to be below the SML with low or negative alphas.

IMPLICATIONS OF THESE TRADING STRATEGIES

1. CAPM correctly computes required risk premiums 
Investors are systematically ignoring positive NPV investment opportunities, because either there is lack of information or the cost of implementing strategies is higher than the returns to be earned

2. CAPM doesn’t correctly compute risk premium 
The market porftfolio is inefficient such that the stock’s beta does not adequately measure the market risk, but the investors are bear risk unknowingly, thus the returns the earn are not excess (alpha) but merely the compensation for taking on additional risk

Why are some market portfolios not efficient?

Proxies such as S&P 500 maybe inefficient in a true market scenario, because there are stocks which have nonzero alphas.

Investors who are biased towards large growth stock, who are attracted by news coverage alone, and don't maintain a balance between small, value and momentum stocks.

Investors who care about characteristics other than the volatility of stocks, for example, the probability of extremely high dividends, may choose portfolios that are inefficient.

There's quite a variety in the number of methods available to firms in order to estimate the cost of capital. One of the most commonly used one is the CAPM model. The others are used by companies that prefer a different style of approach, that best curtails to their circumstances, conditions and needs. These methods are the previously mentioned 'Multifactor model'. Also, by using the historical average returns of the firm, and lastly, the dividend discount model, which is not that commonly used by many firms. All of these methods depend on the organization and its type, and the sector is operates in. i.e: The CAPM model is more commonly and likely to be used than smaller firms. In addition to that, the model is also quite simple to implement and tends to provide reliable results.

CAPM assumption that a market is always efficient is false

Investors ambition is to beat the market by earning +ve alpha[a]

Does not imply that CAPM conclusions are void.