Reading: Introduction to Diversification

To conclude this section, let us extend the considerations from before. Now that we know how to compute the risk and return of a portfolio, nothing can stop us from forming additional portfolios with different weights. That's exactly what the following graph does.

The green line shows the risk-return pattern when we move from 100% bonds (red dot) to 100% equities (blue dot). The green dot on this line marks the portfolio that we have computed before, i.e., 40% equities and 60% bonds.

As we can see, the risk-return profile improves substantially when we add a little bit of equities to a bond portfolio: Moving out of the bond portfolio, the risk initially drops even further while the return increases. Clearly, these portfolios are preferable to a pure bond portfolio, as the earn higher returns at a lower risk! At some point, the classical risk-return trade-off kicks in and additional returns can only be achieved with a higher risk.

We can also use this graph to underpin the important role of the correlation. The dashed lines in the graph shows the risk-return pattern with different assumed correlations (from +1 to -1). Most notably:

• If the returns are perfectly positively correlated (\(\rho=1\)), there is no diversification potential. As a result, the risk-return trade-off assumes a linear function that connects the two portfolio constituents.
   
• In the other extreme, if returns are perfectly negatively correlated (\(\rho = -1\)), we have perfect diversification. We can completely eliminate the risk! In our example, that would be the case with an allocation of approximately 28% to equities and 72% to bonds.

When building portfolios, we are therefore ideally on the outlook for assets that have low correlations, as these assets offer the best diversification potential.