理解alpha、beta、ir 基金指标||mutual funds、hedge Funds、Public Offering Fund

• Indicators of Investment Risk

  There are five main indicators of investment risk that apply to the analysis of stocks, bonds and mutual fund portfolios. They are :

  1. alpha

     Alpha is a measure of an investment’s performance on a risk-adjusted basis. It takes the volatility (price risk) of a security. Or fund portfolio and compares its risk-adjusted performance to a benchmark index. The excess return of the investment relative to the return of the benchmark index is its alpha.

     An alpha of 1.0 means the fund has outperformed its benchmark index by 1%. Correspondingly, an aloha of -1.0 would indicate an underperformance of 1%.

  2. beta

     Beta is a measure of the volatility, or systematic risk, of a security or a portfolio, compared to the market as a whole.

     Beta is calculated using regression analysis and it represents the tendency of an investment’s return to respond to movements in the market.

     By definition, the market has a beta of 1.0.

     A beta of 1.0 indicates that the investment’s price will move in lock-step with the market. A beta of less than 1.0 indicates that the investment will be less volatile than the market. Correspondingly, a beta of more than 1.0 indicates that the invesetment’s price will be more volatile than the market.

     Conservative inwestors who wish to preserve capital should focus on securities and fund portfolios with low betas while investors willing to take on more risk in search of higher returns should look for high beta investment.

  3. r-squared

     R-squared is a statistical measure that represents the percentage of a fund portfolio or a security’s movements that can be explained by movements in a benchmark index.

     R-squared values range from 0 to 100. Accoding to Morningstar, a mutual fund with an R-squared value between 85 and 100 has performance record that is closely correalted to the index.

  4. standard deviation

     Standard deviation measures the dispersion of data from its mean.

     Basically, the more spread out the data, the greater the difference is from the norm. In Finance, standard deviation is applied to the annual rate of return of an investment to measure its volatility (risk).

     A volatile stock would have a high standard deviation. With mutual funds, the standard deviation tells us how much the return on a fund is deviating from the expected returns based on its historical performance.
     $$StandardDeviation=\sqrt{\frac{{\sum }_{i=1}^n(x_i-\hat{x}{)}^2}{n-1}}$$

  5. Sharp ratio

     The Sharp ratio measures risk-adjusted performance. It is calculated by subtracting the risk-free rate of return (U.S. Treasury Bond) from the rate of return for an investment and dividing the result by the investment’s standard deviation of its return.
     $$Sharpratio=\frac{R_p-r_f}{st{d}_p}$$

  MPT is a standard financial and academic methodology used to assess the performance of equity, fixed-income, and mutual fund investments by comparing them to market benchmarks.

• Volatility

  Volatility is a statistical measure of the dispersion of returns for a given security or market index.

  Volatility is often measured as either the standard deviation or variance between returns from the same security or market index.
  $$variance{\sigma }^2=\frac{{\sum }_{i=1}^n(x_i-\hat{x}{)}^2}{n}$$

• Alpha vs. Beta

  Alpha是针对benchmark的超额收益，是针对return而言；

  Beta是针对risk的，描述portfolio的波动。基准的beta设为1，如果portfolio的Beta也是1，说明其与市场整体基准波动相同。

  相较于Beta仅用于度量volatility，Alpha是个更综合的指标，包括基金经理水平等等。

• Mutual Fund vs. Hedge Fund

  Mutual Fund	Hedge FUnd
  Don’t take share from the profit	Take ~20% perfoemance fee from the profit
  Are available to the general public	Are available only to high-net-worth and sophisticated investors
  Charge a management fee (normally 1-2%)	Charge management fee (nomally 2%) plus performance fee (normally 10-30%)
  Can’t make high-risk investments	Can make high-risk investments
  Tend to perform worse than hedge funds	Tend to perform better than mutual funds

• IR

  Information Ratio (IR, wikipedia) : is a measurement of portfolio returns beyond the returns of a benchmark, usually an index, compared to the volatility of those returns.
  $$IR=\frac{PortfolioReturn-BenchmarkReturn}{TrackingError}$$
  $TrackingError$ : Standard deviation of difference between portfolio and benchmark returns.

  The IR is used to evaluate the skill of portfolio manager at generating returns in excess of a given benchmark.

• References

1. 5 Ways to Measure Mutual Fund Risk
2. Alpha Vs. Beta: What’s the Difference?
3. Mutual Funds vs. Hedge Funds: What’s the Difference?
4. Hedge funds vs mutual funds
5. Information Ratio – IR