History of Finance - Review

Based on Statistics, we can't be always at the top. Whatever we do, we influence the market. So we can't all be winners.

• Pre-Markowitz - make money if your an insider.
• Gerald Loeb 
• the battle for investment survival
• put all your eggs into one basket
• John Maynard Keynes
• Psychological Principle
• The Greater Fool theory
• Beauty Contest Analogue 
•  based on perception, we ask the question: what will the judges judge?
• what do you think the others will think?
• even if I bought at a high price, some other fool will buy at a higher price
• Markowtiz 
• Issue before: How to measure returns
• he introduced risk and how to put up a portfolio and maximize returns
• significant is within the utility curve
• Markowitz Paradox - utility curves 
• Asset universe
• Markowitz -diversification as the risk averse technique
• James Tobins
• optimum portfolio
• don't put your eggs into one basket
• reduce risk using the combination of the risk free rate and others
• we can go outside the Markowitz area
• Simplifying calculus - efficient frontiers labours on calculus
• William Sharpe
• Main feature is the stock market itself
• risk that can be diversified away
• CAPM - Eugene Fama uses the term "one factor model" to describe Sharpe's
• Efficient Market
• Prices fluctuate ramdomly
• Eugene Fama - EMH, 1970
• 1974
• Paul Samuelson
• calls for a benchmark
• if can't beat them, join them
• "Market Portfolio"
• Charles Elis
• Mimic the market - as a proxy for the market
• the use of "index funds"
• it manages the portfolio and costs
• it means no more of the excess returns

Trying to figure out: How to deal with your investments by exerting Alpha.

Alpha - need not to look for weights

• Beta - horizontal
• Alpha - y - intercepts ( excess returns)
• To what degree is the market beatable? Can the market be beaten

Hunt for a better mouse trap

• Multi-factor model 
• Macro-economic Factor Model
• GDP+Analysis => asset allocation
• Industry => asset allocation
• Search for Arbitrage opportunities (buy and sell) and convergence trade (put and call options)
• Search for market anomalies (e.g January effect, small cap effect, low P/B ratios)
• Value vs growth Stocks, underlying stocks Not the company itself
• Contrary strategies
• Risk minimizing modeling (VAR)

References: Searching for Alpha by Ben Warwick

Films: Inside Job, Margin Call, Wall Street Never Sleeps, Wall Street, Too Big to Fail 

MPT and Asset Allocation

Modern Portfolio Theory

It's a good thing the group reported  Modern Portfolio Theory.

Additional Information:

• In the optimization $\text{min } \sigma = w^T V w $, the inputs in the diagonal of the covariance matrix $V$ are variances.
• It is important to ask the questions: How did they defined the data used? What constitutes returns? It is not that simple and we have to be objective. We must based it on empirical data and past research.
• What is the use of the Tangency Portfolio? Why is CAL included in the efficient frontier graph?     

The edited graph are copied in Wiki.


• Every stock's expected return is determined by its beta with the tangent portfolio
• Tangent portfolio by definition has the highest SR
• MPT shows only one method of diversifying: managing risk and return. IRL, there are other ways such as go in and out of the market. Since, CAL connects the risk free rate to the tangency portfolio. The highlighted portion is the combination of the risk-free rate and the tangent portfolio which is found to be a way to diversify with a lower risk and still be in the efficient frontier. 
• Any of the portfolios in the upper portion of the $y^2$ curve can beat the market.
• SML - because everyone is buying the market, risk is how much is the market exposure. 
• Empirical data and results shows that MPT is just as it is, a theory. No one can really define and measure the "global market". Some even tested the capacity of CAPM and it doesn't work.

Exercises - found in MPT.xlsm for more info

1. Optimization $\text{min } \sigma = w^T V w $ in Excel. 

2. Covariance

Ways of getting covariance:

In class, we got the covariance of two stocks using the long way and the short way. Details are in the excel sheet. It contains 10 stock returns with an n of 99.

• =COVARIANCE.S(array1, array2)
• =COVARIANCE.P(array1, array2)
• =SUM(x-u_x)(y-u_y)/n

Covariance Matrix

It was also analyzed how the covariance came up to be. 

• It is the matrix multiplication of the mean adjusted return transpose by the mean adjusted return then divided the number of returns
• In short: =mmult(MARTranspose, MAR)/N

Somehow, there are some discrepancies on the numbers I computed for the matrix to the QuantProf, the predefined function made my my prof. But it is very small. Later I found out that some defined =mmult(MARTranspose, MAR)/(N-1) to solve for the covariance matrix.

Other references: Quantitative Methods in Finance by Watsham 

Asset Allocation

• Policy Statement should be there in every portfolio.
• Over long periods of time, sizable allocation to equity will improve results.
• Asset allocation determines your return. It is the overall asset allocation that is important.

Other references involve the previous research material used and a ppt presentation made by another group.

Searching for Alpha

Good reference: Searching for Alpha by Ben Warwick

• History of Finance: Review
• Important people that helped in shaping up the Finance world
• We are trying to figure out how to deal with our investments. Are we satisfied with the the allocation? To what degree is the market predictable? 
• Instead of looking for the weights, we look at alpha.
• where alpha is the excess returns, y-intercepts
• beta is the slope.
• Hunt for a better trap
• Multi-factor model 
• Macro-economic Factor Model
• GDP+Analysis => asset allocation
• Industry => asset allocation
• Search for Arbitrage opportunities (buy and sell) and convergence trade (put and call options)
• Search for market anomalies (e.g January effect, small cap effect, low P/B ratios)
• Value vs growth Stocks, underlying stocks Not the company itself
• Contrary strategies
• Risk minimizing modeling (VAR)

Modern Portfolio Theory Slides

This is to review for the Modern Portfolio Theory. It is made by our group in TSP class.

Also read Paul Willmotts FAQ's on Modern Portfolio Theory. He's simply amazing at explaining materials. The article is on the the pages area for reference sake. Oh, I still have to review on the Matrices on MPT. Add it to the list of things to do.