Question

1. Explain the components of the single index model, linking diversifiable and systematic risk to your answer. What is the Security Characteristic Line and what information does it convey? What is the information ratio and what important information does it convey? Is the full covariance efficient frontier or the index model efficient frontier better?

Answer 1

(i). Components of Single Index Model : It is an asset pricing model and according to this model returns on security can be represented as a linear relationship with any economic variable. It can be represented as follows:

Rs - Rf = + (Rm - Rf) +

where, Alpha represents abnormal returns for the stock.

Beta shows systematic risk

and represents unsystematic risk.

(ii). Security Characteristic Line: It is a line which is straight and formed using regression which gives an idea about a particular security's systematic risk and return. We can create this line by plotting a security's return at various points.

Y-axis shows excess return whereas X-axis shows excess returns of the risk-free rate.

It gives infomation about a security's performance with respect to markets performance. It gives visual picture of how a security's performance is relevant to the markets performance.

(iii). Information Ratio: It is the measurement which is used to measure a portfolio's return beyond its benchmark. we use this ratio to measure level of portfolio manager's skill and ability whether he/she can generate excess return than given by its benchmark or not.

Formula to calculate it:

Information Ratio = (Portfolio return - Benchmark return) / Tracking error

Important information that IR provides is that it tells us about the skill and ability of a portfolio's manager, and if IR comes high it suggests that portfolio manager's skills are good enough to outperform benchmark.

It also gives information about how much a fund has exceeded the benchmark.

(iv). Full co-variance frontier is better than index one.