Question

The risk free rate is currently 7.6%. Use the data in the accompanying table for the Flo family's portfolio and the market portfolio during the year Just ended to answer the questions that follow (C Data Item Rate of return Standard deviation of return Beta Fios' Portfolio 12.7% 13.1% 1.37 Market Portfolio 9.2% 1.00 a. Calculate Sharpe's measure for the portfolio and the market. Compare the two measures, and assess the performance of the Fios' portfolio during the year just ended. b. Calculate Treynor's measure for the portfolio and the market. Compare the two, and assess the performance of the Fios' portfolio during the year just ended c. Calculate Jensen's measure (Jensen's alpha). Use it to assess the performance of the Fios' portfolio during the year just ended d. On the basis of your findings in parts a, b, and c, assess the performance of the Fios' portfolio during the year just ended. a. The Sharpe's measure for the Fio portfolio is. (Round to two decimal places.) The Sharpe's measure for the market portfolio is(Round to two decimal places.) Based on the computed Sharpe's measures, the Fio portfolio's performance is b. The Treynor's measure for the Fio portfolio is The Treynor's measure for the market portfolio is Based on the computed Treynor's measures, the Fio portfolio's performance is C. The Jensen's measure for the Flo portfolio is %. (Round to two decimal places.) Based on the computed Jensen's measure, the Fio portfolio d. On the basis of your findings in parts a, b, and c, the Fio portfolio Vto the market's performance. (Select from the drop-down menu.) (Round to two decimal places.) Round to two decimal places.) Vto the market's performance. (Choose from the drop-down menu.) the market. (Select from the drop-down menu.) the market during the year just ended. (Select from the drop-down menu.)

Answer 1

Sharpe’s Measure

It is the ratio of average return of portfolio in excess of risk-free assets to the risk of the portfolio. It measures how much excess return a portfolio earn for a given level of risk. Portfolio with high sharp’s ratio believed to be good.

$Sharpe's ratio = \frac{R_{p} - R_{f}}{\sigma _{p}}$

Where,

Rp = Return of Portfolio

Rf = Risk free Return

$\sigma _{p}$ = risk of portfolio (standard deviation)

Treynor’s Measure

It measures the risk-adjusted return based on non-diversifiable risk i.e Beta. It is the ratio of average return of portfolio in excess of risk-free return and Beta. Here, Beta is measure of systematic risk, risk that could not be diversified.

$Treynor's ratio = \frac{R_{p} - R_{f}}{\beta _{p}}$

Where,

Rp = Return of Portfolio

Rf = Risk free Return

$\beta _{p}$ = Beta of portfolio

Jensen’s Measure

It is a measure of risk-adjusted performance of a portfolio. It measures average return of portfolio in excess of portfolio return as per Capital Assets Pricing model (CAPM) model. It is also referred as Alpha.

$Alpha = R_{p} - [{R_{f}+\beta (R_{m}-R_{f})}]$

Where,

Rp = Return of Portfolio

Rf = Risk free Return

$\beta _{p}$ = Beta of portfolio

Please refer below spreadsheet for calculations and answers.

Formula reference -