# Modern Portfolio Theory and Capital Market Theory

- Modern Portfolio Theory (MPT) was born out of a 1952 academic paper by Henry Markowitz; this theory gave us a model of the risk and return of an investment

- Crucially, MPT gave us the Efficient Frontier (see graph) which allows us to identify portfolios with the best risk return trade off; i.e. the most return for the least risk.

- Capital Market Theory (CMT) was born out of MPT. Where MPT gave us a model for the connection between risk and return, CMT gave us a model of how investors will behave in a "MPT" world

- An important assumption of MPT and CMT is that investors will identify and invest in portfolios on the efficient frontier to maximize their risk/return trade off

- The graph to the right shows us the risk (horizontal axis), return (vertical axis) tradeoff for a series of individual securities

###### Why the "Market" is the most "efficient" portfolio

- If I take the graph above, delete everything except the green curve, and trace a straight blue line from the expected portfolio return of a risk free asset (e.g. short term government debt) to the point tangent with the green curve, I will have traced the Capital Market Line (CML)

- Recall, each point along the green curve represents a portfolio with the most efficient trade off of risk for a given level of return; the risk free portfolio on the other hand i.e. the base of the blue line, by definition has zero risk and a nominal return

- It turns out that combining a risky portfolio and a risk-free portfolio clearly improves the risk/return trade off of the resulting portfolio; you can see this by picking any point on the green curve and noting that there will always be a point on the blue line above or even with the green curve; this means that for any portfolio on the green curve; there is a portfolio on the blue line with a better risk adjusted return

- An interesting implication of the CML is that if we assume investors behave according to CMT and MPT by actively attempting to maximize their risk/reward trade off
; no fancy strategy is required to find the optimal risky portfolio, it's right there in front of us**then the optimal portfolio simply becomes the market as a whole**

- The reasoning goes like this:

- The risk-free rate on the y-intercept is same for everyone

- If I can combine the risk-free asset with some portfolio on the green curve, then I can enhance my risk/return trade off (every point representing a portfolio on the green curve has a corresponding portfolio on the blue line that has a better risk/return trade off)

- This blue line only represents varying combinations of a risk free portfolio and a risky portfolio

- Therefore, the best
**risky**portfolio on this green curve will be the point of tangency with the blue line and the; You can't invest in anything above the blue line because there's nothing there to invest in, and investing anywhere else along the green curve or under the green curve will yield less optimal results

- Going back to our base assumption of investors actively attempting to maximize their risk/return tradeoff means that investors will buy this tangent portfolio; aggregating all investors in the market and all investable assets will leave us with a portfolio that is exactly the market portfolio

- The important point about the CML, CMT, and MPT for my purposes here is that it implies that optimal portfolio is some combination of the market as a whole and a risk-free asset; nothing more.

###### Why do people try to pick stocks and why is stock picking is so hard

- People try to pick stocks for all kinds of reasons but there's no evidence that I am aware which says they can be successful with any reliable consistency; success defined as consistently superior risk adjusted returns

- Here's the basic reason why we think this is

- First, you need to understand 2 types of risk:

- Unsystematic risk is defined as that risk associated with securities that can be reduced by diversifying your portfolio; e.g. you can reduce your risk in 1 investment by simply adding another
- Systematic risk is what's left over after you've diversified away as much risk as you can; it's risk inherent to all markets and investments and cannot be reduced by adding any more investments

- When we add additional securities to a portfolio we can reduce diversifiable, i.e. nonsystematic risk, while maintaining the same return; rationally we would continue adding securities until this nonsystematic risk is minimized so that we have the maximum return for the least level of risk

- We are then left with a portfolio only containing systematic risk; we cannot get rid of systematic risk through added diversification

- In the paper "Diversification and the Reduction of Dispersion", JL Evans and Stephen Archer found that combining a portfolio of 15-20 stocks, reduces "dispersion" of returns, (i.e. risk) asymptotically to a min; later studies have found this number to be perhaps as high as 50 stocks

- An interesting conclusion is that investors are not rewarded for the unsystematic risk that they take; if they were then they would bid up the prices of securities with high unsystematic risk knowing that they can then diversify that risk away and still get the return; unfortunately this would raise the prices of stocks with high unsystematic risk which would then eliminate that very return they seek!

- Therefore, my primary focus is on the systematic risk and helping my clients take the appropriate amount of systematic risk using diversified instruments such as Exchange Traded Funds (ETFs). Why would you take avoidable risk that you won't be compensated for? That's what buying unsystematic risk, i.e. undiversified stocks, means.

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I hope you enjoyed my philosophy! Please reach out with any questions you have!