Chapter 1: A brief history history of risk and return

Question 1

1.1 Returns

Answer 1

• Total Dollar Return: Return on an investment measured in dollars that accounts for all cash flows and capital gain(or loss).
• TDR: Dividend Income + Capital Gain (or loss)
  DividendShares + (P2 - P1)Shares
• If you hold stock you should consider the capital gains as part of the return, it is a cash gain.

Question 2

1. Returns

Answer 2

• Percentage Returns: How much do we get for each dollar we invest?
  1. Dividend Yield: The annual stock dividend as a percentage of the initial stock price. This says that for each dollar we invest we received x cents in dividends.
  Dividend Yield= Dividends / P1
  2. Capital Gains Yield: The change in stock price as a percentage of the initial stock price. This means that for each dollar invested we got x cents in capital gains.
  Capital Gains Yield= (P2 - P1) / P1
  3. Total Percent Return: The return on an investment measured as a percentage that accounts for all cash flows and capital gains(or losses).
  Percentage Return (Rate of Return)= Dividend Yield + Capital Gains Yield.
  Percentage Return (Rate of Return)= Div + (P2 -P1) / P1

Question 3

1. Returns

Answer 3

• Effective Annual Return (EAR): The return on an investment expressed on a per-year or “annualized” basis.
  1+EAR= (1+Holding Period Percentage Return)^m ->m=# of holding periods in a year.
  HPPR= (P2 - P1) / P1

Question 4

1.2 Historical Return

Answer 4

• Total Market Capitalization (Market Cap): Stock Price * number of shares of stock. It is the total value of the company’s stock.
  Large companies are called “large-cap” stocks, small companies are called “small-cap” stocks.

Question 5

1.2 Historical Return: Average Annual Returns

Answer 5

Investment Average Return
Large Company Stocks 11.7%
Small Company Stocks 17.7%
Long-Term Corporate Bonds 6.5%
Long-Term Government Bonds 5.9%
US Treasury Bills 3.8%
Inflation 3.1%

Question 6

1.2 Risk Premiums

Answer 6

• Risk Free Rate: The rate of return on a risk-less investment.
  Government borrows money issuing debt with bonds,one form of bonds is Treasury Bills, they have shortest time to maturity of the types of bonds. T-Bills are risk free because when government borrows it can print money or raise taxes to pay back.
  *Excess Return: Difference between risk-free return on T-Bills and risky return on common stocks.
• Risk Premium: The extra return on a risky asset over the risk-free rate; the reward for bearing risk.

Question 7

1.2 Historical Return: Average Annual Returns & Risk Premiums

Answer 7

Investment Av Rtn Risk Prem
Large Company 11.7% 7.9%
Small Company 17.7% 13.9%
Long-Term Corp Bonds 6.5% 2.7%
Long-Term Gvnt Bonds 5.9% 2.1%
Treasury Bills 3.8% 0.0%

Question 8

1.4 Return Variability

Answer 8

• Variance: Common mesure of volatility, measures the average squared difference between actual returns and average return. The bigger this number, the more actual returns tend to differ from the average return. Also, the larger the variance or standard deviation is, the more spread out returns will be.
  Var(R)= ∑(Return - Return Average)^2
• Standard Deviation: Square root of the variance is used because the variance is measured in squared percentages and thus is hard to interpret. The SD is an ordinary percentage.
  SD(R)= √Var(R)

Question 9

1.5 Arithmetic vs Geometric Averages

Answer 9

• Geometric Average Return: The average compound return earned per year over a multiyear period. Tells what you actually earned per year on average compounded annually.
  Geometric Average Return=[(1+R1)x(1+R2)x…x(1+RN)]^1/N-1
• Arithmetic Average Return: The return earned in an average year over a multiyear period. Tells what you earned in a typical year.
  Arithmetic Average Return= (R1%+R2%+…+RN%)/N
• The arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.

Question 10

1.5 Arithmetic vs Geometric Averages

Answer 10

• The arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.
• Blume’s formula combines the 2 averages.
  R(T)= [(T-1/N-1)Geom Av] / [(N-T/N-1)Arithm Av]

Question 11

1.5 Dollar-Weighted Average Returns

Answer 11

• Dollar-Weighted Average Return: Average compound rate of return earned per year over a multiyear period accounting for investment inflows and outflows. Shows how to calculate the return of an investment when an investor makes deposits and withdrawals. This calculation is known as the internal rate of return (IRR).
• The Geometric Average ≤ Arithmetic Average (always), Geometric Average can be greater, less or equal to Dollar-Weighted Average (depending on when deposits/withdrawals are made).

Question 12

1.6 Risk & Return

Answer 12

• The risk-free rate represents compensation for waiting (called Time Value of Money).
• On average if we are willing to bear risk, we can expect to earn a risk-premium. Investments has “wait” component (TVM) and a “worry” componen (risk-premium).
• Risky investments do not always pay more than risk-free investments, that is exactly what makes them risky. There is a risk premium on average but over any particular time interval, there is no guarantee.
• Some risks are cheaply and easily avoidable, and no reward is expected for bearing them. It is only those risks that cannot be easily avoided that are compensated (on average).