Efficient Frontier and Diversification

Those optimal portfolios which provide the highest return for a given risk make up the Efficient Frontier. A portfolio can help reduce idiosyncratic risk but not systemic or market risk.

We discussed how to build a portfolio in our blog “Portfolio Construction and Rebalancing.” In this blog, we will review a few key financial engineering concepts and explain how portfolios can help reduce stock specific risk.

Efficient Frontier (EF): This is the envelop of optimal portfolios that provide the best risk-reward tradeoffs. The dots in the chart are individual portfolios that may include many asset classes (see “Types of Asset Classes” for more information). Imagine drawing a vertical and horizontal line from an individual portfolio to the EF curve. The EF portfolio on this vertical line will provide a higher return for the same risk as does the individual portfolio. Likewise, the EF portfolio on the horizontal plane, like the individual portfolio, will provide the same return but at a lower risk. Risk and potential return increase as you move up the EF, as evidenced by the higher equity allocation (labelled as Aggressive Growth) in the portfolios towards the top of the chart.

Capital Market Line (CML): Short-term U.S. Treasury issued securities such as T-Bills are used as a proxy for cash and are considered risk-free. Hence, they also offer the lowest return (Rf) as marked in the chart. CML is the tangential line from this risk-free return point to the EF curve. The point of tangent represents the market portfolio, which conceptually includes all securities in the market. Market indices are close approximations of a market portfolio. The points on the tangent represent portfolios with different proportions of market portfolio and T-Bills. The Risk Premium is the excess return the market (Rm) provides over the risk-free return.

Risk (β): β is the measure of volatility of a security in comparison to the market portfolio. It is defined as the covariance of the security and the market, normalized over market risk.

β = COV (R,Rm) / σm2

β is 1 for the market portfolio and >1 for securities that are riskier than investing in the market. β will be <1 for less riskier securities.

Capital Asset Pricing Model (CAPM): This is a derivative of the Modern Portfolio Theory, for which Harry Markowitz won a Nobel prize in 1952. CAPM specifies the expected return of a security in an efficient market.

R = Rf + β(Rm – Rf)

This shows that securities riskier than the market (β >1) will earn a higher Risk Premium and hence will have higher return than the market portfolio.

A portfolio reduces Specific Risk (or Idiosyncratic Risk), which is the risk from owing an individual asset (e.g., stocks). This risk can be diversified away by owning a basket of assets. For example, the chart shows that 90% of Specific Risk can be eliminated with a portfolio of just 5 stocks. However, Systemic Risk (or Market Risk) cannot be reduced through diversification. You would be taking on this risk by simply participating in the market.

We specialize in tax-free retirement strategy and investments such as IUL, Annuity and LTC. Prefer a quick and complimentary consultation? Just email us at Karthik@FinCrafters.com

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