Classic risk indicators for investment portfolios - Investments

Classic risk indicators for investment portfolios

Consider the indicators that are often used to assess and compare the portfolios of investment (financial) assets.

1. The reward to variability ratio, RVarR.

This coefficient shows the additional yield (premium) received by the investor with respect to the risk-free rate per unit of total risk. As a measure of overall risk, the standard deviation of portfolio returns is taken as follows:

where - the estimated return on the asset or portfolio (for example, for the year); - the risk-free rate of return as the yield accepted for the risk-free asset.

The higher the Sharpe ratio, the better the results of portfolio investment. Portfolios can be ranked by the Sharpe ratio.

2. The reward to volatility ratio (RVolR) , in contrast to the Sharpe ratio, does not consider the overall risk as an indicator of risk, but only its systematic part, expressed through a measure of the beta coefficient:

The higher the Traynor coefficient, the better the investment results for the portfolio.

3. Portfolio diversification index. The portfolio diversification level is estimated by correlation of the portfolio and the corresponding market index (usually separately for stocks and bonds). The square of the correlation coefficient is the coefficient of determination (R 2 ). The coefficient of determination shows that share of variability in the variance of portfolio returns, which is explained by market profitability (market index change). If the portfolio is completely diversified, then the coefficient of determination is equal to unity and its profitability is fully explained by the change in the market.

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4. Alpha Jensen (Jensen), or a measure of unsystematic risk. The coefficient alpha (a) is calculated on the basis of the market model linking the premium for investment in the portfolio ( k p - kp ) with a premium for systematic risk, which is proportional to the beta coefficient of the portfolio. alpha shows a reassessment or underestimation by the market of the systematic risk of a portfolio (or an individual asset) .The market model:

where MRP is the market premium for risk as the excess of the yield of a well-diversified portfolio over the risk-free rate (see Chapter 15).

In regression, alpha is an additional member that reflects the quality of portfolio management. Since CAPM is the equilibrium model (in more detail the CAPM model and the beta-factor calculation is described in Chapter 15), the average market quality of the portfolio management guarantees a risk premium proportional to the beta- coefficient. Alpha reflects the contribution of the portfolio manager to the actual premium received. If the alpha coefficient in the regression is statistically significant and positive, then it can be stated within the framework of the CAPM hypothesis that portfolio results are better than average market. If the alpha coefficient in the regression is statistically significant and negative, then analysts conclude that the portfolio results are worse than the average market.

5. Sortino Ratio (SR) is similar to the Sharpe ratio, but instead of the overall volatility of the portfolio, so-called down volatility is used as a one-way deviation of yield. For the Sortino coefficient, volatility is calculated from the yield values ​​that fall below the minimum acceptable level. MAR (Minimum Acceptable Return) - the minimum allowable level of portfolio return, for example, the average return observed earlier on the portfolio or market yield.

The modified Sortino coefficient is calculated relative to the risk-free rate, i.e. as the minimum acceptable level of profitability is the average risk-free rate.

To calculate the average yield of a portfolio (), the geometric yield formula is used as the natural logarithm of the price ratio (logarithmic yield).

The indicators of risk and return of individual portfolios compare with each other, as well as with market indices. For example, the MICEX and RTS index ratios are used as benchmark benchmarks, index ratios RUX-Cbondsu RBM (United States Bonds Market) - for bond portfolios. Indices can be applied for individual industries, local markets. The results for a particular portfolio are compared with the results of a close "on spirit" (a set of securities) of the index.

Example 9

The information agency compares the results of collective investment funds with the MICEX index. The company RICH Consulting compares the stock funds with the RTS index, the bond funds - with the RBM index, and the mixed investment funds - with the "mixture" RTS indices and RBM in equal proportions.

The culture of informing investors involves the disclosure of the above coefficients with a certain periodicity (for example, by years, quarters, months). Comparison of the coefficients allows us to evaluate not only the ratio "risk-return", but also the skill of portfolio managers.

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In Table. 5.2 provides estimates of portfolio risks of collective investment funds (mutual funds of shares and bonds) of the investment company "Troika Dialog" in comparison with the index characteristics (for shares - RTS index, for bonds - index RUX-Cbond).

Table 5.2

Risk indicators of portfolios formed in the United States market (estimates for ruble quotes for the year ended December 29, 2007)



Equity Fund Dobrynya Nikitich

RTS index

Bond Fund "Ilya Muromets"

Bond Fund "Sadko



Standard deviation,%




















Upside potential (U-P) *






* Upside potential - upside potential up as a relative gap between the projected assessment of assets in the portfolio and the current value.

The above factors can not explain, due to which the best result is obtained for various portfolios. To understand the reasons that led to successful results, and assess the possibility of their use for further use, analysts work with factor analysis. An important conclusion that can be obtained from factor analysis is whether the result is random.

Factor analysis of the effectiveness of investment management (portfolios) reveals the importance of certain factors of the external environment and internal management in obtaining financial results.

For factor analysis, multifactor models are traditionally used, for example, the PREFAN model of the consulting company BARRA. The following components of the return from active portfolio management are considered: market tracking, sectoral risk, sector analysis, individual selection of securities.

Confidence levels (confidence level) are statistical estimates of the probability that the estimated value (for example, industry risk, management quality) is not zero (statistically significant). The level is in the range from 0 to 100%. The higher the confidence level, the more likely that the result of the investment is random. Usually, the confidence level is shown in parentheses with the analyzed factors ensuring achievement of the result. A trust level of more than 90% is considered acceptable.

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