Which of the following statements are true:
1. The Kappa family of indices take only downside risk into account
II. The Treynor ratio provides information on the excess return per unit of specific risk
III. All else remaining constant, the Sharpe ratio for a portfolio will increase as we increase leverage by borrowing and investing in the risky bundle
IV. In the market portfolio, we can expect Jensen's alpha to equal zero.
Kappa indices, which include the Sortino ratio and the Omega statistic, consider semi-variance, ie variance calculated only in respect of the downside risk instead of variance (which includes both upside and downside). This is because one criticism of other risk adjusted performance measures is that they take both upside and downside risk into account, even though a portfolio manager or investor is only concerned with managing the downside. The Kappa indices consider returns that are below a threshold to measure performance by. Therefore statement I is correct.
The Treynor ratio is calculated as [(Portfolio return - Risk free return)/Portfolio's beta]. It therefore calculates the excess return per unit of systematic risk and not specific risk. Therefore statement II is not correct.
Increasing portfolio leverage, ie borrowing to invest more in the portfolio, will increase the excess return of the portfolio in a linear fashion. However, it will also increase the volatility of such a portfolio in an identical linear way. Since Sharpe ratio is the ratio of 'excess returns' to standard deviation, the Sharpe ratio will stay constant. In other words, leverage does not impact Sharpe ratio, which is an attribute of this measure that allows us to compare performance across managers and funds regardless of leverage used. Statement III is not correct.
Jensen's alpha results from security selection, ie from specific risk the manager has taken. In a market portfolio, all specific risk is diversified away and only systematic risk remains. Therefore, statement IV is correct.