# The Optimal Portfolio

A tangency portfolio, according to Shiller, is the ultimate takeaway from modern portfolio theory (MPT).  According to the MPT, the efficient frontier represents the maximum expected return that an investor can expect for a given level of risk.  We can infer the converse rule and say that the efficient frontier tells us a level of risk that we must accept in order to receive a quantified expected rate of return.  Always remember, when we consider the risk of a portfolio, we consider the overall portfolio risk and not the risk of the individual securities within the portfolio.

When we hold the risk free asset in a portfolio, we can create what is known as the tangency portfolio, which is the most efficient one possible from a mathematical perspective.  It takes a lot of theory and math to get there, but the conclusion is that the tangency portfolio is the entire market of investable securities.  This has some assumptions that are not found in the real world, such as the idea that all investors are rational and will choose the most efficient investments possible.  Even so, the theory can teach us a useful way to think about how portfolio risk works.

We can draw a straight tangential line between the riskless assets (which has a standard deviation of zero) on a graph to a hypothetical mutual fund that contains the entire market for everything.  That line forms a continuum from zero risk if we invest in nothing but the riskless asset (and die poor) to the point of maximum risk where we hold none of the riskless asset (and have many sleepless nights).  We can pick any point along that line that represents the amount of risk we will tolerate.

That risk corresponds to an expected rate of return.  If we really want to take on some risk (and possibly go bankrupt), we can extend the line beyond merely investing our own money in the risky asset and invest borrowed money (margin) in the risky asset.  So long as we can find a fool to loan us increasing pools of money, we can increase our potential return to an absurd point.

### ex-ante

This Latin phrase means “before-the-fact,” and is used similarly to “a priori.”  It is used to signal that a statement is a prediction about the future based on past data, and the actual future may turn out to be very different from the prediction.

For various reasons, real portfolio managers cannot buy a little of everything as the EMH suggests.  It the real world, the trick is to search for investments that have minimal risk and a high probability of a (preferably high) real return.  The other trick is to find assets that are not correlated with the assets that you already have in your portfolio.  Keep in mind that risky assets have their own unique volatility, but most movement will be as a group.  When the S&P 500 is down 3%, for example, nearly every stock you look at will be down to some degree (described by beta).  This means that diversification only works to the degree that we choose uncorrelated assets.

The most dangerous scenario for the average person is thinking that they have a diversified portfolio when they really do not.  True diversification should be verified by mathematical means.  The easiest method to ensure true diversification of risk is with portfolio optimization software.  All you have to do is plug in the ticker symbol of the fund and the allocation that you are thinking, and the software will tell you what the biggest drawdown of the portfolio was for the longest lookback period for which data is available.

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`Last Updated: 6/25/2018`

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