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)