About CAPM and Treynor vs Sharpe ratio PDF

Preview

Summary

- More about CAPM
- More about Sharpe ratio
- Topic: Risk and return...

Description

Measuring Expected return: Measuring for individual assets or non-diversified portfolio  use CAPM Measuring for diversified portfolio (e.g. market portfolio)  Make direct estimate (i.e. calculate arithmetic mean for ST investors and geometric mean for LT investors)

Sharpe ratio VS Treynor ratio Sharpe ratio Looks to measure reward per unit of systematic risk -

Aims to reveal whether an investment is more worthy than a risk-free investment by measuring reward per unit of total risk (systematic risk + idiosyncratic risk) of the investment. As long as Sharpe ratio has positive value  the investment is better than the risk-free investment

Not accurate when comparing individual assets or non-diversified portfolio  individual assets contain idiosyncratic risk + systematic risk, and, Sharpe ratio does not ”filter out” the presence of the idiosyncratic risk. So Sharpe measures reward per unit of total risk (systematic risk + idiosyncratic risk). It is not fair to compare between idiosyncratic risks  hence, Sharpe ratio should not be used.

Measuring reward per unit of risk for market portfolio  can use Sharpe ratio or Treynor ratio (Since market portfolio does not contain idiosyncratic risk to begin with, when calculating reward per unit of risk, the “risk” can be total risk or only systematic risk – does not make a difference).

Treynor ratio Looks to measure reward per unit of systematic risk Used when adding individual assets to diversified portfolio  since idiosyncratic risk of individual asset will be diversified away once added to the portfolio, it is accurate to just take into account systematic risk in the individual asset (i.e. what is the asset’s reward per unit of systematic risk) 



If you compare Treynor ratio of individual asset A with Treynor ratio of individual asset B, you are only comparing Asset per unit of Systematic risk for each asset (idiosyncratic risk not taken in account). If you compare Sharpe ratio of individual asset A with Sharpe ratio of Individual asset B, you are comparing their Asset per unit of Total risk  Total risk contains both idiosyncratic risk and systematic risk. It is not a fair comparison as it does not make

sense to compare the idiosyncratic risks between two assets, since future idiosyncratic risks are unpredictable and past idiosyncratic risks are not representations of future idiosyncratic risks. If you really must compare the Reward per unit risk between individual assets, it is still more accurate to use Treynor ratio  because you at least know what is each asset’s Reward per unit of Systematic risk.

In conclusion: Denominator of Sharpe ratio = asset’s risk (standard deviation of asset’s return = systematic risk + idiosyncratic risk) Denominator of Treynor ratio = asset’s risk in relation to the market (beta = systematic risk only) Numerator for both ratios = Asset risk premium = Expected asset return – Risk-free rate...