Chapter 1: A Brief History of Risk and Return

For the purpose of forecasting future returns: -The arithmetic average is probably __ for long forecasts -The geometric average is probably __ for short forecasts

"too high" "too low"

Percent Return on Stock

(Dividend Income + Capital Gain (or Loss)) / Beginning Stock Price

Arithmetic Averages versus Geometric Averages

-The arithmetic average tells you what you earned in a typical year -The geometric average tells you what you actually earned per year on average, compounded annually.

You buy 200 shares of Kylo Companies, Inc. at $30 per share. Three months later, you sell these shares for $31.50 per share. You received no dividends. What is your annualized return?

1 + EAR = (1 + holding period percentage return)^m m= the number of holding periods per year m= 12 months/3 months = 4 1 + EAR = (1 + 0.5000)^4 = 1.2155 EAR= 0.2155 or 21.55%

2 components of Total Dollar Return

1. cash received directly while you own 2. value of asset may change

Categories of Financial Investments

1. large-company stocks 2. small-company stocks 3. long-term corporate bonds 4. long-term U.S. government bonds 5. U.S. Treasury Bonds

Sakaar Inc. has had the following returns over the last four years: 10%, 10%, -20%, 25% What is the arithmetic return for the last four years? What is the geometric return for the last four years?

Arithmetic Returns (0.10+0.10+(-0.20)+0.25)/4 = 6.25% Geometric Returns ((1+0.1)x(1+0.1)x(1-0.2)x(1+0.25))^(1/4) - 1 = 4.88%

Equation for finding the Total Dollar Return on a Stock

Dividend Income + Capital Gain (or Loss)

You buy 200 shares of Kylo Companies, Inc. at $30 per share. Three months later, you sell these shares for $31.50 per share. You received no dividends. What is your return?

Return = (P(t-1)-P(t))/P(t) = ($31.50-$30)/$30 = 0.5000 = 50% --> holding period percentage return

The Second Lesson of Returns

The greater the potential reward, the greater the risk. (positive correlation)

The First Lesson of Returns

There is a reward, on average, for bearing risk.

Percent Return

Total Dollar Return on a Stock / Beginning Stock Price

Suppose you invested $1,400 in a stock with a share price of $35. After one year, the stock price per share is $49. Also, for each share, you received a $1.40 dividend. What was your total dollar return? Your Total Percent return?

Total Dollar Return: $1,400/$35 = 40 Shares Dividends = 40 shares x $1.40 = $56 Capital Gain = 40 Shares x ($49-$35) = $560 Total Dollar Return = $560 + $56 = $616 Total Percent Return: Dividend Yield = $1.40/$35 = 4% Capital Gains Yield = ($49-$35)/$35 = 40% Total Percent Return = 4% + 40% = 44%

Geometric Average Return Answers the question:

What was your average compound return per year over a particular period?

Arithmetic Average Return answers the question:

What was your return in an average year over a particular period?

Variance

a common measure of return dispersion. Sometimes, return dispersion is also called variability. -measures average squared difference between actual returns and average returns

Normal Distribution

a symmetric, bell-shaped frequency distribution that can be described with only an average and a standard deviation.

Dividend Yield

annual stock dividend as a percentage of the initial stock price = D (t+1) / P(t)

The total percent return is the return for ___ invested.

each dollar

Capital Gains Yield

the change in stock price as a percentage of the initial stock price = (P(t+1)-P(t))/P(t)

Risk Premium

the extra return on a risky asset over the risk-free rate; that is, the reward for bearing risk

Risk-Free Rate

the rate of return on a diskless investment

Effective Annual Return (EAR)

the return on an investment expressed on an "annualized" basis

Total Percent Return

the return on an investment measured as a percentage of the original investment (rate of return)

Total Dollar Return

the return on an investment measured in dollars, accounting for all interim cash flows and capital gains or losses. *if you buy an asset of any type, your gain (or loss) from that investment is called the RETURN on your investment.

Standard Deviation

the square root of the variance -sometimes called volatility -in the same units as the average