Assignment on Market Efficiency

Faculty of Economics and Business Department of Business FINANCE I (102329) – Groups 4 & 53 – 2013-‐14 Dr. Joan Montllor & Dr. Maria-‐Antonia Tarrazon

Wenwen Xi

Diego Ivan Barros Marc Mataix Sanjuan

Assignment on Market Efficiency, Noise, and Behavioural Finance Relate the assessment by Fisher Black

Noise makes it very difficult to test either practical or academic theories about the way

that financial or economic markets work. We are forced to act largely in the dark.

with the evaluation of the impact of efficient markets theory and behavioral finance made

by Robert J.Shiller.

Professor Black is a heavy supporter of the efficient markets theory. This theory states that price in the stock market is set as a function of the information related with its true value. Noise is defined as the irrelevant information that some investors include as relevant but is unrelated with the true value of a given asset. Hence, trading this type of information creates inefficiencies in the market. If there was no noise in the market, the market will not exist. That is because if everyone has the same information, the will not be double coincidence of wants. Noise crates high volatility in prices and because of that, Proferssor Black states that “Noise makes it very difficult to test either practical or academic theories about the way that financial or economic markets work. We are forced to act largely in the dark.” Traditional finance ignores the research for investors’ actual decision-‐making behavior. The rise of behavioral finance theory break the fundamental assumption of traditional finance theory, based on a psychology research, proceeding from actual decision-‐making psychology of real investors. With the development of behavioral finance, behavioral economists and experimental economists have proposed numerous paradoxes. The traditional "rational man" assumption has been unable to explain the reality of economic life and behavior. It is consistence with the evidences to assume the general public to behaves totally rational. Many investors often make trading decisions based on "noise" rather than the relevant information. They are easily effected by suggestion from financial experts suggest and will not divert investment, often traded with self-‐righteousness and transformed the portfolio in the hands frequently. It is not as efficient market theory finds that, public trading passively as they lack information. Behavioral finance believes that when arbitrageurs trade, they are not only facing the risks of changes in underlying factors, but also the noise trading risk. There are two theoretical basis of behavioral finance: one is limited arbitrage, the second is investor psychology analysis.


From the first premise, traditional finance believes that arbitrage plays a key role in achieving market efficiency. Even the irrationality of investors exists and stock prices deviate from the basic value, there are still rational arbitrageurs, which eliminates the former influence on prices. However, behavioral finance believes that, the “perfect” arbitrage is actually quite limited due to the fact that the noise trader risks, etc. It weakened its influence on market efficiency. Viewed from the theory of the second base, although limited arbitrage explains why market is inefficient with the interference of noise trader, it cannot tell us what specific form is taken by this inefficiency. Due to this, we need the establishment the second theory. There are two major reactions in the market, which are overreaction and under reaction. In response to these two reactions, experts of behavioral finance proposed some models of investors’ behavior based on psychology. According to the behavioral theorists, we are not longer assuming that we act to dark but rather to continue investigate investors, not assets, to turn the dark into bright color.

Assignment on the CAPM. 1. Explain the meaning of the market portfolio, its relationship with the separation

theorem and with market indices as well as how it influences investors’ decision making.

(No calculations are required to answer this part of the question). Why does the market

portfolio of Khalersburg yield an expected return of 14.1415% with an associated

variability of 11.8279%?

The market portfolio is a weighted average of the sum of all assets that exists in a market.

The separation theory, according to Tobin, states that if an investor can lend and borrow at

the same rate, the market portfolio will always be the same. In other words, if an investor

can lend and borrow at the same rate, they will choose the same proportion they invest in

the assets of the market in combination with the risk free asset.

The market portfolio of Khalersburg consists of four stocks, which own their own expected

return and associated risk. The total expected return will be the weighted average of the

expected rate of returns of all the assets in the Khalersburg market. That is,

𝐄𝐑𝐦 = 𝟎.𝟑𝟑𝟔𝟔𝟖𝟓 ∗ 𝟎,𝟏𝟐 + 0,𝟐𝟐𝟗𝟎𝟐𝟔 ∗ 𝟎,𝟐𝟎 + 𝟎,𝟏𝟗𝟏𝟕𝟐𝟑 ∗ 𝟎,𝟐𝟓 + 𝟎,𝟐𝟒𝟐𝟓𝟔𝟔 ∗ 𝟎,𝟎𝟑 = 𝟎,𝟏𝟒𝟏𝟒𝟏𝟓

The volatility of the market can be explained by the weighted average of the individual

volatilities plus the relationship among them. That is, the weighted average of the

volatilities plus the covariance between the stocks.


2.Calculate the coefficient beta of stock 3 using covariances. Explain the meaning of

coefficient beta and its significance in financial markets. Which is the correlation

coefficient between stock 3 and the market portfolio? What does it mean? Finally, relate

β3 to βM.

The beta of the security 3 is 2.18. That is, when the market changes 1 basic point, the

security changes 2.18 basic points. The correlation between the stock and the market is

0.049504618. This means that the stock is has a very light positive dependence with the

market. Hence, when beta m, which is nothing else than the market variance, changes the

stock reacts in the same way 2.18 times.

3.Why does stock 3 promises an expected return of 25%? Calculate the risk for which the

expected return on stock 3 offers a risk premium. In case that this risk premium does not

compensate for total risk, explain why.

We can calculate the require return of the stock that is part of M using the Security Market

Line:

𝑅𝑗 = 𝑟𝑖𝑠𝑘 − 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒 + 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑟𝑓 + 𝐸 𝑟𝑚 − 𝑟𝑓 ∗ 𝛽𝑗

0.25 = 0.05+ 0.141415− 0.05 ∗ 2.187820434

If we assume that there is no diversification, we can calculate the required rate of return

using the Capital Market Line. That is:

0,25 = 0.05+0.141415− 0.05

0.118279 ∗ 𝑋 = 0,3038124

For the same level of return of 25%, we can obtain a risk of 30% in the Capital Market Line.

The stock has a risk 50% that means that the risk premium is 20%. That is because in the

Capital Market Line we assume perfect diversification and hence, the specific risk of the

particular stock is eliminated.


4. Break down the risk of stock 3 justifying the relationship among the different types of

risk associated to it.

We can break down the risk as follows: The total risk is equal to the systematic risk plus the

specific risk. Everything has to be squared.

That is:

(𝜎!)! = (𝛽! ∗ 𝜎!)! + (𝜎(𝑒𝑗)!

In the case of the stock 3, that is:

0,5! = (2.19 ∗ 0.118270)! + 𝑋

𝑋 = 0.4276834653

This means that this stock has a risk of 6,7% due to the intrinsic risk of the market where it is

trade and a risk of 42% associated with the specific value of stock 3.

5. Mr. Pepet Canons decides to invest 10.000 € assuming a total risk of 50%. Design an

efficient investment for him on the Kahlersburg stock exchange that copes with his

preference. Calculate the expected rate of return his investment portfolio, its composition

and the amount of Euros that Mr.Canons invests in stock 3 efficiently.

If we assume that the CAPM theory holds, we will use the Capital Market Line to asses the

return of the investment of Mt Canons because the CAPM theory states that M is the

optimal portfolio to invest to. That is,

𝐸(𝑟) = 0.05+0.141415− 0.05

0.118279 ∗ 0,5 = 0,4364379983

The return of the investment of Mr Canons will be 44%.

Continuing with the CAPM we will invest a proportion X in portfolio M that has a return

associated and a proportion (1-‐x) in the risk free asset with its return. That is:

𝑅! = 𝑅! ∗ 𝑥 + 𝑖(1− 𝑥)

0,436437 = 0,141415𝑥 + 0.05 1− 𝑥

𝑥 = 4.2272

That is, Mr Canons will invest 422,72% of his budget or 42272,82€ in M and will borrow

322,72% from the risk free asset or 32272,82€. If the proportion of the stock 3 in the market

is 19.72%, Mr canons will invest 0,1972*42272,82€ in 3. That is a total of 8336,20€.


6. Finally, explain why stock 4 yields less than the risk-‐free asset despite bearing a total

risk of 50%? Is it true that its contribution to σM is negative? What does this imply in

terms of risk reduction through diversification?

Stock 4 has a negative correlation with all the other assets in the market. Because of that,

the return is very low even though the risk is 50%. Yes, it is true that the contribution to the

risk of the market is negative. We can see that calculating the systematic risk:

𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑅𝑖𝑠𝑘 = (𝛽! ∗ 𝜎!)!

(−0.218782 ∗ 0,118279). = −0.02588

This implies that including this stock even if it has a very low return and high risk, since the

correlation coefficient is negative with all the stocks, not only it add less that the weighted

average risk but subtracts risk to the market portfolio.

Assignment on Market Efficiency

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