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2 A Sharpe Line Finding a Place on the Efficient Frontier

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Although Markowitz in 1952 drew the map of the efficient frontier, he still left it up to each investor to find the best place to settle. Some places along the frontier offered low risk and low reward, some high risk and high reward, and some a Goldilocks combination. To each, his or her own.

Markowitz's only advice was to ask for more return with each extra measure of risk taken. Investors should not take risk for free. An investor might put money in a drawer and get just enough return to protect against inflation. But as risk goes up, so should the required return. The amount of additional return might differ for each investor. The adventurous might require a little, the cautious a lot. Markowitz does not prescribe the trade-off.

Markowitz does describe investors as risk averse, meaning not that investors avoid risk but only that investors need more return to compensate for more risk. As risk rises, so does required return. The trade-off that each investor makes between risk and return creates a map of the investor's preferences. A line on that map might start at the point of no risk and return and slope gently or sharply upwards, or it might curve up like an airplane lifting off a runway. For the same level of risk, of course, the investor would take the highest return. That moves the line or the curve up to a higher starting point.

An investor's map of preferred investment risk and return can help the investor or the investor's advisor find a place along the efficient frontier. One line in that map should intersect with the combinations of risk and return that are available along the efficient frontier (figure 2.1). Preference meets reality. At that intersection, Markowitz advised, invest.

Markowitz's advice still left investors with a lot of work to do. Each investor had to figure out risk, return, and correlation of each investment on the infinite list. That led to each investor's own efficient frontier. And the investor still had to figure out the map of risk and return preferences and where those might line up with the investor's own efficient frontier.


Figure 2.1 In Markowitz's world, every risk-averse investor would make a different trade-off between extra risk and extra return and choose a different portfolio.

Markowitz had changed the state of the investment art, but a simple guide to using it would have to wait at least another 10 years.

Competitive Advantage in Investing

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