Performance Measurements

Question 1

What is the Treynor Ratio?

Answer 1

• Treynor = (return - risk free rate)/beta

Question 2

What is drawdown?

Answer 2

• For drawdown there must be a peak and a valley, i.e. there must be high inflection point and inflextion point or there is no drawdown to calculate.
• 10 year drawdown as a percent in each of the following two periods:
  
  • 30 Sep 1995 to 30th Sep 2005 = (107/109)-1=-1.8%
  • 30 Sep 2005 to 30 Sep 2015 = (114/127)-1 = -27.2%

Question 3

What is the sharpe ratio?

Answer 3

• Calculates portfolio return per unit of risk.
• The portfolio with the greatest sharpe ratio delivers the most return per unit of risk.
• Portfolio theory would recommend investing in some combination of the highest portfolio sharpe ration and the risk free rate, depending on investor risk profile.
• Sharpe ratio = (return - risk free rate)/ STDEV

Question 4

Why does the sharpe ratio make adjustments for risk?

Answer 4

• There is a direct lnk between risk and return over the longer term. The higher the risk, the higher the return to compensate for the risk and vice versa.
• Similarly, an investor should require a higher return to compensate for buying a fund with higher risk. It is important to look at return per unit of risk taken by the fund.
• The sharpe ratio largely reflects the strength of the underlying markets that a fund is invested in as well as reflecting manager performance against the markets.

Question 5

What is the information ratio?

Answer 5

• Information ratio = (portfolio return - benchmark returns)/tracking error.
• Info ratio measures a portfolio managers ability to generate excess returns relative to a benchmark by looking at the active bets taken.
• Attempts to identify consistency of fund manager performance.
• The ratio identified if a manager has beaten the benchmark by a lot in a few months or a little every month - because this will be reflected in the STDEV of the return difference.
• The higher info ratio the more consistent a manager has been.
• An index fund would have an IR close to 0 becuase there is no active return.
• Many closet managers would have an IR of +/-0.2
• Rarely is the number +/0 0.05 or more.

Question 6

What is the M2 measure?

Answer 6

• Is equivalent to the return which the fund would produce if it had the same risk as the market as a whole/
• M2 = rf + (stdev of benchmark / stdev of portfolio) x (Portfolio return- risk free rate)
• Fund with the highest M2 measure will have the highest return for any level of risk. The same will be the case for the fund with the highest sharpe ratio.
• Fund rankings based on the sharpe ratio will be the same as rankings based on M2.
• M2 iis effectively a linear transformation of the sharpe rato and does not add any new information.
• Expressed as a % the M2 measures can be explained easier to an investor.

Question 8

What are the merits of the Treynor ratio?

Answer 8

• Treynor uses beta for systematic risk and this is suitable for a diversified investor but can be hard for clients to understand.
• Treynor can be useful for measuring returns across different sectors and for any portfolio where a client holds a number of portfolios.
• Simple cost-benefit comparison of risk and return trade-off

Question 9

What are the merits of the Sharpe Ratio?

Answer 9

• The sharpe ratio is more intuitive to understand and more applicable for clients who may not be fully diversified.
• The sharpe ratio is based on the CML so is appropriate for investors with one portfolios.
• Simple cost-benefit comparison of risk and return.

Question 10

What are the merits of the info ratio?

Answer 10

• The information ratio is a measure of active return, the difference between the portfolio return on the benchmark index, divided by the STDEV of the active return or tracking error.
• Measures a portfolios managers ability to generate excess returns relative to a benchmark by looking at the active bets taken.
• Information ratio also attempts to identify consistency of fund manager performance.
• The ratio identifies if a manager has beaten the benchmark by a lot in a few months or by a little every month because this will be reflected in the STDEV of returns.
• The higher the ratio the more consistent the manager.
• Can be useful indicator of active or passive management style

Question 11

What are the drawbacks of the various ratios?

Answer 11

• Treynor ratio:
  
  • Linked to capital market theory and SML
  • Only allows relative assessment of portfolio performance
  • Difficult to assess statistical significance.
  • Ignores unsystemativ risk in the portfolio.
• Sharpe Ratio:
  
  • Linked to capital market theory and SML.
  • Only allows relative assessment of portfolio performance
  • Difficult to assess statistical significance.
  • Ignores diversification potential of portfolio.
• Jensen’s alpha:
  
  • Difficult to calculate needs formal regression analysis.
  • Diversifiaction of portfolio needs to be assessed separately
  • Alpha and significance can very markedly depending on the specification of model and return generation.
• Information ratio:
  
  • Only allows relative assessment of portfolio performance
  • Difficult to interprest and assess statistical significnace.
  • Assumes that portfolio and benchmark have similar levels of systematic risk.

Question 12

What are the different adjustments for risk taken by the ratios?

Answer 12

• Treynor ratio:
  
  • Portfolio beta relative to market proxy
• Sharpe ratio:
  
  • STDEV of total portfolio return in excess of risk free rate
• Jensen’s alpha:
  
  • Portfolio beta relative to market index proxy or portfolio beta relative to multiple risk factors
• Information ratio:
  
  • STDEV of portfolio return in excess to benchmark index, i.e. tracking error.