8/11/2019 Chapter 1 - FINA

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Chapter 1 : A brief history of risk and return . If you buy an asset of any time, your gain or loss from that investment is the return on your investment.

PV of a growing annuity:

periodsof numbern

period perrategrowthg

period perreturnof rater

paymentfirst

111

P

g r P

PV r

g n

Total Dollar Return : The return on an investment measured in dollars that accounts for all cash flows and capital gainsor losses. = Dividend Income + Capital Gain (or loss). Total dollar return = ($1.40 x 40shs) + 40($49 $35). Totaldollar return = $56 + $560 = $616.

Dividend Yield : The annual stock dividend as a percentage of the initial stock price. {Dividend Income/Org Stock Price}.Dividend yield = $1.40 / $35 = 4%.

Capital Gains Yield : The change in stock price as a percentage of the initial stock price. {(Ending stock price Beginning Stock Price) / Beginning Stock Price}. Capital gain yield = ($49 $35) / $35 = 40%.

Total Percent Return : The ROI measured as a % that accounts for all cash flows & capital gains or losses. = Dividend Yield + Capital Gains Yield. OR (Gain orig investment) / orig investment. Total percentage return = 4% + 40% = 44%

Effective Annual Return (EAR) : The ROI expressed on a per- year or annualized basis.:::: 1+EAR=(1+HoldingPeriod Percentage Return)M (thats to the M power). ------ 1 + EAR = (1 + HPR) m ----- m = the number of holdingperiods in a year.---In this example, m = 1.5 (12 months / 8 months). Therefore: 1 + EAR = (1 + .44) 1.5 = 1.7280. -----EAR = (1.7280) 1. ------So, EAR = .7280 or 72.80%.

Historical Average Return :n

returnyearlyReturnAverageHistorical

n

1i

Large company Stock Stock portfolio based on the S&P 500 index, which has 500 of the largest company in US. Small Company Stock Corresponds to the smallest 20% of the companies listed on the NYSE. Long term corporate bond - Portfolio of high quality bonds with 20 years to mature. Long term US government bonds : Portfolio of US government Bonds with 20 years to maturity.

US Treasury Bills : Portfolio of Treasury Bills (T-Bills) with a 3 month maturity. Total Market Capitalization (CAP) : equal to its stock price multiplied by the number of shares of stock. Risk Free Rate The rate of return on a riskless investment. Risk Premium The extra return on a risky asset over the risk free rate; the reward for bearing risk. Variance : A common measure of volatility or return dispersion. Sometimes, return dispersion is also call variability. Standard Deviation : The square root of the variance. Sometimes the square root is called volatility Var : = The sum of the squared deviations but the number of returns less 1 = .027/(4-1)=.009 Standard Deviation : SD = Square Root of Variance or .009 = .09487 Normal Distribution : A symmetric, bell shaped frequency distribution that is completely defined by its avg & STD Geometric Average Return : the average compound return earned per year over a multiyear period. Arithmetic Average Return : The return earned in a average year over a multiyear period.

Calculating the geometric average return : for numbers 10%, 12%, 3%, -9%. = (1.10 x 1.12 x 1.03 x .91) raised tothe power 1.

o Take each of the N annual return and add a 1 to each after converting to decimal .o Multiple all the numbers from step 1 together .o Take the result from step 2 and raise it to the 1/N power where N is number of components .o Finally, subtract 1 from the result in 3 .

Also you can use this formula : (Ending Compound dollar amount)/(Beginning amountinvested)^(1/N) 1

Which one to use? : The geometric average tells you what you actually earned per year on average compoundedannually. The arithmetic average tells you what you earned in a typically year.

Blumes Formula: A formula used to combine the two averages. R(T)= (T-1)/(N-1) * Geometric average + (N-T)/(N-1)

* Arithmetic average. On this, T is the number of years in the future we are forecasting for. N is observation period

8/11/2019 Chapter 1 - FINA

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