formulae for calculating semi variance wth a worked example

Below-mean semivariance faces some of the following criticisms:

1. The loss of some information in forming the measure

2. The uncertainty in which observations will be retained in the calculation until the sample is selected

3. The difficulty (now resolved) in constructing optimal (mean-semivariance) portfolios, ex-ante

4. The lack of well-established statistical properties for sample semivariance, which inhibits strict statistical tests assuming distributions with semivariance as the proper measure of the second moment

Despite these criticisms, recent evidence supports the value of semivariance as a risk measure:

1. Methods for creating optimal portfolios in mean-semivariance space have been established (Ballesteros)

2. Semivariance risk can be decomposed into systematic and unsystematic risk contributions (Beach)

3. Cross-sectional pricing of semivariance and downside betas are confirmed and generally stronger than for variance and traditional betas (Ang, Estrada)

4. Statistical properties for below-mean semivariance are better established (Satchell)