Finance Numericals

Treynor Ratio:   It measure the risk adjusted rate of return earned after considering the market risk. The ratio named after Jack L. Treynor. The ratio considers the systematic risk. It is same as Sharpe ratio but it consider beta not a standard deviation to measure the performance of an investment fund. Beta is sensitive to market conditions. Higher the ratios better the efficiency of an investment portfolio or fund. Formula: Treynor ratio = R p – R f / β Where, R p = Expected return of a portfolio R f = Risk free rate of return Β = Beta (systematic risk) Advantages of Treynor ratio: ·          It helps to measure the performance of a fully diversified funds in which the unsystematic risk is zero. ·          It helps to rank the investment portfolio. Disadvantages of Treynor ratio: ·          It does not consider total risk to measure the performance of a fund. ·          It is not suitable for undiversified portfolio. Difference between Sharpe

Sharpe Ratio:   It is derived by William F. Sharpe in 1966. It measure the risk adjusted return of a portfolio.  It helps to determine the efficiency of an investment portfolio. The ratio measure the excess return earned by investors by investing in a risky investment. The higher ratio indicates that the investment portfolio gives better return to its holder.If volatility of an expected return is higher than the Sharpe ratio will be low. Formula: Sharpe ratio = (R p – R f ) / σ p Where, R p = Expected return of a portfolio R f = Risk free rate σ p = Standard deviation of a portfolio Advantages of Sharpe ratio: ·          It is simple and easy to calculate. ·          It measure the risk adjusted return of a portfolio. Disadvantages of Sharpe ratio: ·          It does not differentiate between systematic risk and unsystematic risk. ·          It does not give accurate result because it based on historical data. ·          The risk of the portf

  Portfolio correlation: The correlation states that how much one stock is related to other stock. It measure on the scale of +1.0 to -1.0. If the two stocks have +1 correlation it means both the stocks are positively correlated and if the return of one stock decreases then the return of other stock also decreases in same manner. If both the stocks have 0 correlations it means the two stocks are not correlated it means the return of one stock is increases the other stock does not show the same effect. If the two stocks have -1 correlation it means they are negative correlated and if the return of one stock increases then the return of other stock decreases. Correlation shows the degree of relationship between two stocks. Formula: R ij = cov ij / σ i σ j Where, cov ij = co-variance between stock i and j σ i = standard deviation of asset i σ j = standard deviation of asset j Portfolio Co-variance: The co-variance states that how two stocks price move in future.

Portfolio return:   It is a return on portfolio earn by an investor or holder of an investment portfolio.  The return includes capital appreciation and dividend. Formula of Portfolio return: E(r) p = Ʃ n i=1 w i *E(r i ) Where, E(r) p = Expected return of a portfolio W i = weight of asset in a portfolio E (r i ) = expected return of a security or stock Portfolio risk: It is a risk of losing return or decreasing the return of an investment due to certain factors. The higher return is expected by investors out of his investment but higher the return means higher the risk. Investors can decrease the risk by diversifying its investment.standard deviation helps to measure the volatility of expected return. Higher standard deviation means the investment is more risky. Standard deviation = √ ( probability (return – expected return) ^2) Example: Calculate the expected return of a given portfolio of A and B: Portfolio Weight of stock

Multi Index Model:   It is a model which includes more than one factor which affects the risk and return of a portfolio. It helps to construct a portfolio. In single index model only one factor affect the securities return that is market return but in this model not only market factor consider but other factors are also consider which help to analyse the portfolio return more accurately. But it is difficult to decide the factors and their quantity.  Advantages of Multi Index Model: ·          It considers more than one factor because it is assumed that not only one factor affects the securities return other factors also have some effects on the assets return. Disadvantages of multi Index model: ·          It is based on historical data which does not help to forecast future return accurately. ·          It is difficult to decide the factors and its quantity included to form this model. ·          It is much more complicated than single index model. Formula: ER