Sharpe Ratio

It is generally believed that an investment portfolio is better constructed the higher its Sharpe ratio (Sharpe Ratio – William F. Sharpe).

The Sharpe ratio describes the relationship between a portfolio’s risk premium and its risk:

Sharpe Ratio = Risk Premium/Standard Deviation
Sharpe Ratio = (Return-Risk Free Rate) / δ

Why is this interesting?

In the graph below, dots represent 1,000 randomized combinations of five different stocks (IBKR, PDD, GOOG, COIN, CROX), showing the trade-off between portfolio return and risk.

The higher and more to the left we are positioned on this “cloud” (the Efficient Frontier), the better the expected return-to-risk ratio of the portfolio (based on 3-year historical data).

On the graph, a straight line (the Capital Market Line) originates from the risk-free rate (10Y T-Bond) and touches the upper part of the cloud.
At the point of contact, the Sharpe ratio reaches its maximum — meaning the portfolio is at its most optimized point.

This straight line is called the Capital Market Line (CML), and it represents the trade-off between risk and return for a portfolio made up of a combination of risky assets and a risk-free asset.
At the point of tangency, you have the optimized market portfolio.

• If you combine this optimized portfolio with risk-free assets (e.g., by buying Treasury bonds), your combined portfolio will move down the line, decreasing both risk and return — but the Sharpe ratio stays the same.
• If you are willing to take on more risk (e.g., by leveraging your position), you can move up the line.

Source: Principles of Corporate Finance – by Richard Brealey, Stewart Myers, and Franklin Allen

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Interesting details:

In reality, the CML relates to the market portfolio, not any individual investor’s portfolio.
Therefore, the more diversified your personal portfolio is, the more your “cloud” will shift to the left, as specific risks are minimized and only systematic (market) risk remains.
(One good diversification strategy is adding real estate to an equity portfolio.)

Also, because we are talking about the market portfolio, at the point of contact (tangency point), the portfolio beta (β) equals 1.

• Above the CML line, β > 1 (higher risk)
• Below the CML line, β < 1 (lower risk)

It’s considered good when the Sharpe ratio is above 1; a ratio near 2 is seen as very good, and near 3 is rare and excellent.

Optimizer in Excel:
In this model, you can optimize across five stocks.
If you are interested, it’s easy to expand the model to include more stocks.
However, keep in mind that this model does not account for dividend statistics, so it’s best suited for stocks that do not distribute dividends.

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