Risk and Return

1
Lecture 7

• Risk and Return

2
Lecture Objectives

• Calculate returns and standard deviation of
  returns
• Expected values and standard deviation of
  expected values
• The concept of risk and diversification
• Quantifying risk
• Beta and the Capital Asset Pricing Model

3
Return and Risk

• Two dimensions to financial decision
• Return Risk
• Investors want to maximise return
• And minimise risk
• Trade off between risk and return

4
Calculating returns

• Calculating return has been covered in previous
  topic
• Where
• Pt Price in time t
• Pt-1 Price in time t-1
• t is the holding period
• the holding period could be a day, a month, a
  year, etc.
• In a similar fashion we can calculate market
  index return. See the example in the textbook.
• Remember that we must include dividends in the
  above calculation

5
Calculating returns

• The above measures single period return. (Say
  daily, monthly, etc). The above return is also
  calculated using historical information.
• Say we calculate the monthly returns for a
  certain company for six months
• Return
• Month 1 10
• Month 2 5
• Month 3 5
• Month 4 3
• Month 5 6
• Month 6 4
• We can calculate the average return and the
  standard deviation of returns for the six month
  for this company

6
Average return and Standard devation
7
Risk

• Risk is uncertainty. The uncertainty of how
  actual outcomes may differ from what is expected.
• In Finance, risk is measured in terms of standard
  deviation of returns.
• In our discussion above, we have used historical
  information to calculate risk. However, past
  risk may not be necessarily a good indicator of
  future risk.
• One way to refine our analysis for risk would be
  to attach a probability to possible future
  outcomes and calculated the expected return (what
  you expect future returns to be) and standard
  deviation of expected return (what you expect the
  risk of the investment to be).

8
Expected Value

• Economic Probability Return on
• Conditions investment
• Boom 0.30 35
• Steady Growth 0.40 20
• Slump 0.30 5
• What is the expected return, that is the long run
  return for this investment?

9
Expected return and standard deviation

• Return(Ri) P(Ri) Ri x P(Ri)
• 35 0.30 10.5 (35 - 20)2 x 0.3 67.5
• 20 0.40 8 (20 - 20) 2 x 0.4 0
• 5 0.30 1.5 (5 - 20)2 x 0.3 67.5
• 20 135
• Expected Value 20
• Standard deviation 11.61
  

10
Partitioning risk

• Invest in a number of securities instead of just
  one Why??
• Should reduce the variability of returns (This is
  the basis of diversification)
• As long as the assets do not move perfectly
  together (perfectly positively correlated), you
  will achieve some reduction in the variability of
  the returns.

11
Systematic and unsystematic risk
Unsystematic risk
Total Risk
Systematic or non-diversifiable risk
As you include more assets into your portfolio,
your unsystematic risk declines.
12
Diversification - an example

• Gains from diversification are only possible on
  securities that are less than perfectly
  positively correlated. If securities are
  perfectly positively correlated than it would
  only result in risk averaging.
• Say you have invested 50 in Share A and 50 in
  share B
• Return on Share A Return on Share B
• 10 9
• 5 10
• 7 6
• 6 15
• Average return 7 Average return 10
• ?A 2.16 ?B 3.74

13
Diversification

• Instead of holding just one of the shares. Say
  we now decide to hold 50 of our holdings in
  share A and 50 in share B
• Portfolio (50 of A and 50 of B)
• Return on portfolio
• (109)/2 9.5
• (510)/2 7.5
• (76)/2 6.5
• (6 15)/2 10.5
• Average return 8.5
• ?p 1.83

14
Characteristic line

• If we regress the return on an asset with the
  return on a market index, we get the
  characteristic line.
• The slope of the characteristic line is called
  beta. It measures the sensitivity of the assets
  return to the return on the market.
• Beta is a measure of risk. Companies with large
  betas are more sensitive to the market.

15
Capital Asset Pricing Model (CAPM)

• A model that prices risk. It gives you rate of
  return you should get given a level of risk.
• The return on the jth asset depends on its beta.
  The return is the risk free rate plus a premium
  for taking risk.