Most investors tend to believe that stocks are a good—perhaps even the best—investment in the long run. However, the reason for expecting good performance from stocks is perhaps not always clearly articulated: Quite simply, it is because they are risky.
For an investor in the US, US Government debt is generally viewed as being risk-free, if we ignore inflation risk. This investor would rank investment-grade senior corporate debt as slightly more risky than Treasury bonds (with AAArated debt viewed as less risky than AA, followed by A, and so on). Next in the hierarchy would come subordinated debt, preferred stock, and common stock would bring up the rear. The reason stocks are the riskiest investment is that they are at the bottom of the pecking order in terms of their claim on the company’s profit or cash flow. But the reason they can also be the most rewarding is that they are entitled to all residual profits, after paying off the other more senior claims in the corporate capital structure.
Generally, investments with higher risk are expected to yield higher returns as an incentive to investors. Here, we do not address the issue of return. We simply focus on the risk of various stock-bond portfolios, and examine how much of this risk comes from their components, and, in particular, from stocks.
We do not know how volatile stocks and bonds will be in the future. We could use historical volatility as a projection, but the realized volatility of any asset depends on both the time period and the horizon over which it is measured. We therefore make some assumptions that are based on the realized values for the period 1975-2016 (the point we are trying to make here does not depend on the exact assumptions).
In Fig.1, we illustrate the assumed volatilities for stocks and bonds, and also the assumed correlation between them. We denote volatility with the Greek letter σ (sigma) and use subscripts ‘s’ and ‘b’ for stocks and bonds, respectively. The correlation is denoted by the Greek letter ρ (rho), with both ‘s’ and ‘b’ as subscripts, denoting that this is the correlation coefficient between stocks and bonds.
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