Topic 6 - Risk and return for individual assets and portfolios

Question 1

The risk premium is

Answer 1

the added return (over and above the risk-free rate) resulting from bearing risk

Question 2

Risk statistics

Answer 2

• There is no universally agreed-upon definition of risk
• The measures of risk that we discuss are variance and standard deviation

The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time. Its interpretation is facilitated by a discussion of the normal distribution.

Question 3

More on Average Returns

Answer 3

• Arithmetic average – return earned in an
  average period over multiple periods
• Geometric average – average compounded
  return per period over multiple periods
• The geometric average will be less than the arithmetic average unless all the returns are equal

Which is better?
* The arithmetic average is overly optimistic for long horizons
* The geometric average is overly pessimistic for short horizons

Question 4

The characteristics of individual securities that are of interest are

Answer 4

1. expected return
2. variance and standard deviation
3. covariance and correlation (to another security or index)

Question 5

Sharpe’s market model

Answer 5

• the covariances between pairs of assets could be caused by the covariance of each asset with a common variable
• if this common variabe is the so-called Market Portfolio, we could explain the return on each assets as a linear function of the return on the market portfolio
  ri = αi + βi . rm + εi

Question 6

Systematic and Non-systematic risk

Answer 6

• Systematic risk: any risk that affects a large number of assets each to a greater or lesser degree
• Non-systematic risk: risk that specifically affects a single asset or a small group of assets
• Non-systematic risk can be diversified away
• Total risk = systematic + non-systematic risk
• For well-diversified portfolios, nonsystematic risk is very small
• Consequently, the total risk for a
  diversified portfolio is essentially
  equivalent to the systematic risk

Question 7

Diversification and Portfolio Risk: Additional insights

Answer 7

• Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns
• This reduction in risk arises because
  worse than expected returns from one
  asset are offset by better than expected returns from another
• However, there is a minimum level of
  risk that cannot be diversified away,
  and that is the systematic portion