Asset performance ranking

In practice there are the tasks concerned with ranking the list of assets according to their investment attractiveness. As a rule, to tackle this problem some sort of performance measure is used. SmartFolio uses several such measures. All of them have a shape of the Reward to Risk ratio. The only difference between the measures implemented in SmartFolio is a formula used in the denominator (Risk). The mathematical meaning of the Reward is the same for all performance measures: it is the difference between the asset excess Mu Equal to Mu plus Dividend yield minus Risk-free rate. and the target excess growth rate The difference between growth rate which the investor demands on his investments and the Risk-free rate. All rates are continuously compounded..    

Analytical portfolio

Instantaneous Information Ratio Performance measure used to compare individual assets. Its numerator is equal to the difference between Excess Mu and Target excess growth rate, and denominator is equal to Volatility. – volatility The most common measure of risk. Defined as annualized standard deviation of returns. is used as a risk measure.

Historical portfolio

Instantaneous Information Ratio – volatility is used as a risk measure.

Normalized Instantaneous Sortino Ratio Equal to Instantaneous Sortino ratio adjusted in such way that under the assumption of independent normally distributed logarithmic returns it coincides with Instantaneous information ratio. – downside volatility Similar to the notion of Volatility, but accounts for only those price increments which do not exceed the threshold. Semi-volatility is its special case corresponding to the threshold equal to the average increment size. The usage of downside volatility instead of ordinary volatility is justified when the distribution of logarithmic price increments deviates from normal. In the latter case downside volatility better reflects risks of the investor. is used as a risk measure.

Normalized Instantaneous STARR Ratio Equal to Instantaneous STARR ratio adjusted in such way that under the assumption of independent normally distributed logarithmic returns it coincides with Instantaneous information ratio.  – Conditional Value-at-Risk Conditional expectation of losses beyond VaR (measured in % of the initial wealth) over a given time interval at a given level of statistical confidence. is used as a risk measure. This is the most suitable performance measure for assets with substantially non-normal distribution of returns.

Note. Under the assumptions of the analytical model all above performance measures coincide. This is why the instantaneous information ratio is the only measure implemented for the analytical portfolio.

Asset ranking algorithm

  1. Construct the portfolio based on assets you wish to rank.  

  2. After you formed the portfolio, you can find all performance measures listed above in the MAIN table.

  3. To complete the operation you should sort the table by a corresponding column.

Important! Ordinary ratios, besides instantaneous ones, are also commonly used in literature. The difference is that ordinary ratios have expected excess growth rate Expected instantaneous rate of return (including Dividend yield) over the risk-free rate. instead of excess Mu in the numerator. The main difference in the usage of these classes of performance measures consists in the following:

  • If compared assets are supposed to be used as components of a continuously rebalanced portfolio, then instantaneous ratios become more appropriate as performance measures.

  • If one compares already formed portfolios, rather than separate assets, then their relative investment attractiveness should be measured with ordinary ratios.

In the former case, when selecting portfolio components, the investor has an opportunity of combining them with each other and with the riskless asset Other notations are Risk-free asset or Numeraire. It is the asset, in units of which portfolio wealth is measured. As a rule, the investor is nearly indifferent to changes in value of the riskless asset.. On the contrary, in the latter case one considers the portfolios as separate alternative investments, thus depriving the investor of the continuous rebalancing advantages. For further details see [Nielsen, Vassalou; 2004].

Ordinary measures are used in SmartFolio with respect to portfolios only. They are presented on the PORTFOLIO SUMMARY table.