There is a Connection between OIB and the price in the very short horizon - it takes time for the market to react

Negative conditional Serial correlation: - Prices are not unconditionally serially correlated
-Given OIB, there is however a significant negative serial correlation
-That is, if you know the last period order imbalance is positive (buyer initiated trades)
-Current price is expected to increase
-Next period price is expected to decrease
→ Negative conditional serial correlation

Reason:

• Market makers adjust the quotes to much when OIB > 0. Perhaps to be safe?
• In the Next period the price falls on average
  
  

Conclusion:

• Prices are not strong form efficient. May suggest that marketmakers are not optimally performing? Could have exploited the systematic reversal by adjusting quotes more efficiently
• The market is efficient With respect to other market paraticipants

Factors:

• “Soft investment factors”: clear decision-making, capable portfolio manager, and consistent investment philosophy
• Past performance
• Past return volatility
• “Service factors”: capabilities of relationship professionals, usefulness of reports prepared by the fund manager, effective presentations to consultants
• Fee
• Assets Under Management (AUM)
  

Conclusions

• Consultants'’ behavior confirms our worst fear
• Rely on insignificant or counterproductive information
• Highly successful in generating asset flow, changes in recommendations generates more flow
• Fail miserably in spotting winners
  

Benchmark:

• Manager receives h2(x-b)’r where b is benchmark and x the chosen portfolio
  

Benchmarking does not align the interests of the manager with those of the investor

The manager invests some in the benchmark rather than in the optimal portfolio

Solution?:

• He therefore invests such that the benchmarking is completely canceled out
• and only the optimal portfolio remains
• The manager achieves a more balanced “portfolio”
• The investor gets a suboptimal Portfolio
  

The investor is better of giving the manager a share of the Portfolio.

When the uninformed holds the index Portfolio. Market Portfolio is only efficient when uninformed holds the market portfolio

When the prices are 100% efficient - We know from Grossman & Stiglitz that prices cannot be fully efficient!

Too many investors think they can beat the market portfolio, and hold inefficient portfolios in stead of the index

If suboptimal porfolio is a result of difference in taste -> permanent inefficiency
If suboptimal Portfolio is a result of differences in belief -> temporary inefficiency

In an efficient market there is only one risk factor - the market (CAPM). However we know that there are numbers of anomalies affecting Returns (book-to-market ratio, share issuing, net size, accruals, momentum, change in assets and profit etc.. )

If market is fully efficient - all information is reflected into the price. There would be no incentive to acchieve information since it has no value at all

Stock prices move in discrete intervals, both in time and value. The assumtion of contioneous time and contineous prices is however convenient in Mathematical terms. It is also a fairly good approximation - we therefor often model Stock price movements as contioneous process.

This means that it if it is a long time until expiry date, then an option has some value, even if the price is lower than the exercise price since it is always a possibility that the option will pay out as long as we are not at the expiration date.

American: you can choose whether you wish to exercise the option before the terminal date

European: the option can only be exercised on the terminal date.

In general:

• A Call option is in the Money when St > X and out the Money when St < X
• A put option is in the Money when St < X and out the Money when St > X

When St = X then the option is at the Money for both option types

• One can combine the purchase and sale of puts and Calls With different exercise price, to design some special cash flow at different share prices.
• When taking into account the intrinsic value a combination will provide cash flow as long as the Stock price is between "a" and "b". Possible to use this information in order to Place a bet that the price of some Stock will be within a certain Level (Telenor example)
• Similary one can use options to bet that the price is going to be different, positive or negative, from a specific target - imagination is the only limit to cash flows that is possible to obtain.

By issuing Stock options a Company can provide management With strong incentives to increase the value of the shareholders and thus the share price, without the need to dilute shareholderst interest to much today.

To strong insentives? Short term thinking priority over long term?

Difficult tho seperate Luck from actual ability (CEO example - pure Luck?)

if it is easy for managers to beat the market - it is not efficient. Most scholars agree the market are not strong form efficient, the interesting tests are within the two first.

Tests for correlation. If there are any covariance/correlation between the change in price today to tomorrow and the change from yesterday to today, it means that yesterdays price carry information about today.

Two interpretations of the medium term momentum and short term reversal effect:

1. Either it suggest that the market overreacts slowly to News, and so over a 3-12 month time the price increase more than the index. In the subsequent years the effect is reversed back to correct Level.
2. Alternatively momentum is compensation for risk - you can make Money betting on last years winners, high Returns often is a result of a Company that have experienced important events during the year (mergers, aquisitions or New Products). Potential gains not realized? The market requires a preimium to hold promising Companies. The reversal may be explained by a decline in risk Premium when real implications of events are better understood by the market.

Small firms tend to outperform bigger firms - goldmines or risk Associated With such firms? Types of risk:

• More Public information on larger firms
• Small firms often illiquid and expensive to trade (Premium cost)
• Compensation for unobserved risk, why has the Company declined in value?

Book to market (B/M): - Firms With high book value tend to outperform other Companies. Is the Company undervalued?

• Companies are often undervalued because they have few "Growth" prospects. These will deliver stable Return but there is no "Growth option"
• younger Companies often have better Growth options, hence they are often assigned With a higher valuation

A possible explanation can be that risk increases after anouncements. The Stock price is however not acting as expected if this was the case. If risk Premium was the reason one would expect gradual increase in price after the announcement in the case of bad News as well. Since this is not what is observed - it is more likely that post earnings announcement drift is evidence that the market is not perfectly semi strong efficient.

Returns are affected by net size, accruals, change in asset profit etc. Difficult to explain in terms of risk premium

It would be strange if private information could not been used to generate excess Returns. Hence, the little evidence that exists here suggests insiders do have a advantage.

It is likely that the difference is due to different views on the assets volatility through the market.

These are interconnected/related. If prices are jumpy then volatility is not constant!

With constant volatility, deviations from the mean will always be normally Distributed by the Law of large numbers. When it is not, it suggests that the Returns are drawn from a different distribution With different variances.

Stock prices have normal distribution With 3 different variance regimes (higher peak and fatter tails)

For Equity the volatility smile is often skewed, With lower implied volatility for high strike prices. The explanation has to do With leverage. All Equity is leveraged, since Companies are financed With debt as well as Equity.

• when the price of the Equity is low, the leverage (debt to Equity ratio) increases. Hence the issuers of options find the options find the more risky and charge a higher price.
• opposite if price is high and leverage low, then the risk is low and so will the option price be.

If the irrational investors are a relatively small Group, these constrains will not eliminate the markets ability to exlopit these traders. However, however rationality is a widespread and the number of rational traders i small, then the rational traders woud need to take large positions to fully exploit the arbitrage possibility.

• Hence, - contrains on credit and short trading limits the opportunities for arbitrage

Active investors cannot outperform the markets as a Whole.

• Active investors holds the market Portfolio, but have higher costs than those just holding the index. In that sense the market is efficient.
• It might be the case that some of the active investors are irrational and lose consitently, but that is hard to imagine that the majority of traders can be this over time, since even With limits on arbitrage these traders would lose consistently over time.

All alternatives/actions can be ranked in order of preference (indifference between two or more is possible).

• It is not uncommon that humans have hard time to deciding between the alternatives, but that often is the case of indifference, and not the ability to rank.
• Some rare exeptions, like deciding who should die (not subject to rationallity and therefor not economics)
  

If A is prefered over B, and B is prefered over C, then A is prefered over C.

• It is sometimes observed that that People either change their preferences over time or just dont understand Choice - preference reversal? Is Limited information the cause to this?

Independence of irrelevant alternatives - if the set of options are (A,B,C) and A is prefered, then A would still be prefered if the alternatives only was (A,B).

• Highly Associated With transitivity.
• a real world example is the sunk cost fallacy - old car, repairs?. The purchase amount is a sunk cost that is irrelevant, but many would think that if they did not repair, they would "lose" the initial Investment from buying the car

For irrationality to explain the anomalies in Finance, those anomalies need to be a result of the stated assumptions (completeness, trasitivity, independene).

Distinction between irrationality and mistakes. Mistakes can be corrected over time.

• the idea of "irrational" traders causing market anomalies is probably misleading. A more likely explanation is that People make mistakes.

Misjudging probabilities - pople are terrible at it:

• Overconfidence - once a person has made a decicion, he tends to overestimate the probability that he is right. People also overestimate their own abilities.
• Small samples - People put to much weight on small sample evidence. Healing and technical analysis example.
• Forecasting - put to much weight on recent experience compared to the full history/data.
• Conservativism - People tend to slowly update their beliefs

Might be helpful if market participants are not rational. Not helpful when rational market since price history are weak form efficiency.

A few common mistakes:

• Framing - a decicion may rely on how the answer is formed.
• Mental accounting - it is cognitive easier to asses different decicions seperately rather than a Whole. Different Investment Portfolios for pension, childre - the optimal would be to manage them as one.
• Prospect theory - assumes that the utility function has a S shape and depend on current wealth. People are loss averse, a loss is felt twice as hard as a winning is positive. Loss aversion mean that you are willing to impose risk to avoid a loss. A interesting property: risk averse to gains and risk seeking on losses!

Techical analysis might be possible, but only when teqhniques are not well known.

No academic evidence that it produces excess Return. Increases risk, which again increases expected Return. A explanation why it Works for someone. Impossible to test it statistically.

Some technical trading Methods:

• Dow Theory: Three different trends (the primary, the secondary and tertiary trend.
• Moving averages: A sliding moving average of Stock prices to find signals for when to buy and sell.
• Volume: Number of Stocks in the market. Both the volume in order books as well as volume of transactions. If a rise happens With little volume it is likely due to New information.

APT was Introduced due to the shorcompings of CAPM.

• CAPM = Eri = RF + beta(rm-rf)
• The biggest assumption under CAPM is that in equilibrium everyone holds indentical Portfolios. We know this is not true.
• Second CAPM is only based on one factor, there is evidence suggesting that expected Returns depend on more than only the market factor.

Difference between APT and CAPM:

• Main difference between the two is that in APT we consider difference to the mean rather than difference to the risk free Return. APT is more flexible since it does not require everybody to hold the same Portfolios. Under APT one can add any factor as explanatory variable in addition to the market index. The most imortant assumption of APT is the one regarding no arbitrage.

The difference is that the left term is not an expection (E) as in CAPM.

Idiosyncratic risk
ei represents the undexplained asset Return. The idiosyncratic Return is not correlated With any known factot that affects the other assets. It is therefor uncorrelated With other assets. This meaning:

• Total varaiance of this idiosyncratic risk is simply the sum of the idiosyncratic contribution from each asset in the Portfolio: var(1/n ei)=1/n^2*sigma^2e
• As the number of assets n increasesm the total idiosyncratic variance will deminish (well diversified Portfolio). For large enough n the variance is nedligible.

Assume we have two large well diversified Portfolios, A and B With zero idiosyncratic risk. Lets assume both have factor betas Equal to one:

• ra = muA + F
• rb = muB + F
  now consider buying A and selling B. Return would then be:
• ra - rb = mu A - mu B, since the diversifiaction removes all risk, this implies an arbitrage opportunity if the net Return is positive. The investors would neutralize this effect by buying one and selling the other, creating equilibrium again.
• With only one factor, all variation in Return should in equilibrium be explained by different exposure to that factor.
  

We can add factors, such as maro-economic factors (GDP, gross Investment, % change in inflation), but it can also be Properties that can sort Stocks in different categories (Return of small relative to big firms, HML, excess Returns of corporate bonds over government bonds). Assume Portfolios A and B each depending on a distinct factor, With factor loadings (beta) Equal to one;

• ra = mu a + 1*F1
• rb = mu b + F*2

A Portfolio that Depends on only one factor With factor loadings Equal to one, in a universe of several factors, is called a factor Portfolio.

In order to construct independent factor Portfolios (factor Portfolios that depend on only one factor each), we need to decompose the covariance Matrix by finding its "eigen vectors".
Want to construct Portfolios that the covariance of each factor is zero. Since we want A and B to be independent factors With zero correlation/covariance. The independent factor Portfolios are just a tool to explain why differences in Return have to be explained by differences in factor loadings.

Arbitrage opportunities With two factors:
Assume a investor holds a Portfolio that Depends on both factors With loadings Beta1 and Beta 2

• rp = mu p + Beta1F1 + Beta2F2
  Say we sell Beta1 of A and Beta2 of B. The net Return is then
• rp - Beta1ra - Beta2rb = mu p - Beta1mu a + Beta2mu b
  The Return is independent of the factors, because the terms Beta1F1 and Beta2F2 are canceled out when we subtract B1ra og B2rb.
• In equilibrium all variation in expected Returns is explained by different exposure to factors

The arbitrage pricing theory tells us that Portfolios are in general dependent on various factors:

• rp = mu p + Beta 1F1 +Beta2F2 +...+ BnFn
• if all investors hold the same Portfolio, there can be only one factor; the market index. But investors do not hold identical Portfolios!
• The factors do not have to be independent as discussed earlier.
• An additional strenght og ATP is that it does not require many strong assumptions.

Introduced two factors:

• SMB: the smallest Companies in the index minus the largest
• HML: the Companies With the highest book-to-market value minus the Companies With lowest such ratio

ri = alfa + Bm(rm-rf) + BsmSMB + BhmlHML + ei

• turns out that it is very sucsessful in explaining excess returns
• gains from betting on HML or SMB are potentially quite big
• the effect of transaction costs might lower this return
• the strategy of betting on long term factors (SMB and HML) just barely beats a Equal weightet Portfolio, that is before transaction costs
  

Grossman - Stiglitz Paradox:

1. Information value "c" will be zero. If there are no noise traders there is no incentive to be informed.
2. If information is costly, no investor will aquire it if it has no value.
3. All investors in the market will then face a undertainty Equal to the unconditional variane: var(u) = sigma^2theta + sigma^2Epsilon
4. In that case, it will be an advantage for some investor to lower the variance they face to: var(u,theta)=sigma^2epsilon, by aquring information.
5. If however someone aquire information "theta", this will be observed from the change in prices, and information value is again at zero Level.
   The conlusion is that without noise traders there is no unique equilibrium. That beeing said, the market efficiency Grossman & Stiglitz are talking about is strong form efficiencym which are dubtly. Whith strong efficiency all private information is reflected to the priec