Week 2 - Shares, Risk and Return

• What are the two components of return on a share?

  Capital gains and dividend payments
• How is the return on a share calculated?

  Return = Gain in Wealth / Initial Wealth
• If the price of a share at time t is $P_t$ and at time t-1 is $P_{t-1}$, how is the return expressed?


  $R_t =$ \frac{P_t - P_{t-1} + D_t}{P_{t-1}}
• What does the numerator in the return formula represent?

  It captures your gain in wealth
• What does the denominator in the return formula represent?

  It captures your initial wealth
• What is the formula for Wealth Relative (WR)?

  WR = End of period wealth / Beginning of period wealth
• What does WR(t) indicate if it is greater than 0?

  It indicates a positive return
• If an investment of £96 yields a total value of £100.50, what is the return in pence?

  Return = 10050 - 9600 + 300
• How is the Wealth Relative over multiple years calculated?

  It is the product of WRs for each period
• What is the Wealth Relative for 2009?

  WR(2009) = 0.9375
• What is the Wealth Relative for 2010?

  WR(2010) = 1.15
• What is the annualised return if compounded over two years gives a return of 1.078?

  AR = 0.038 or 3.8%
• What is the difference between risk and uncertainty?

  Risk has known probabilities; uncertainty does not
• What characterizes a discrete probability distribution?

  It has a finite number of outcomes
• What must the sum of probabilities in a discrete distribution equal?

  It must equal one
• What characterizes a continuous probability distribution?

  It has an infinite number of outcomes
• How is probability expressed in a continuous distribution?

  As the area under the curve
• What are the two measures needed to describe a distribution?

  Mean and standard deviation
• How is the mean return of share X calculated?

  Mean = $\bar{R} =$$E(R) =$$\sum p_i R_i$
• What is the formula for variance of return for share X?

  Variance = $\sigma^2 =$$\sum p_i (R_i - \bar{R})^2$
• What is the variance of the return of share X?

  Variance = 0.02987
• What is the standard deviation (risk) of share X?

  Standard deviation = 0.173
• What are the steps to calculate the expected return and variance for share X?

  • Calculate the mean return: $\bar{R} =$$E(R) =$$\sum p_i R_i$
  • Calculate the variance: $\sigma^2 =$$\sum p_i (R_i - \bar{R})^2$
  • Calculate the standard deviation: $s =$$\sqrt{\sigma^2}$
• What are the characteristics of discrete and continuous probability distributions?

  Discrete:

  • Finite number of outcomes
  • Probabilities sum to one

  
  

  Continuous:

  • Infinite number of outcomes
  • Probability expressed as area under the curve
• What are the implications of risk and uncertainty in investment?

  Risk:

  • Known probabilities of outcomes
  • Can be quantified

  
  

  Uncertainty:

  • Unknown probabilities
  • Difficult to assess