Expected Rate of Return
Expected Rate of Return [E(r)] = (Rate of Return 1 x Probability of Return 1) +(r2xPb2)+(r3xPb3) etc.
It's an average of each possible rate of return, adjusted by the probability of each return actually happening.
Variance
The difference between the actual return and the expected return, squared
Variance in Rates of Return = [(Actual return 1 - Expected Return)^2 x Probability of Return 1] + [2...]+[3....] etc.
Variance is the average squared difference between possible ret
Standard Deviation
the square root of the variance
How to Calculate the Variance and Standard Deviation for a set of possible rates of returns
(Variance in Rates of Return Equation) but broken down into steps for each possible return
1) Calculate the Expected Rate of Return (using Expedited Rate of Return Formula [E(r1)]
2) Individually subtract E(r) from each possible return (r1) ... (r2) etc.
Probability Distribution
list of possible returns, spread along a bill curve where least likely +/- are on top and bottom, and most likely is in the center.
Measuring Variance and Standard Deviation of Common Stock
1) Calculated Expected Return
2) Take each possible return and subtract E(r), & square each difference
3) Multiply each difference by it's probability of occurring
4) =sum(step3) ? variance
5) Square Root(Step 4) ? Standard Deviation of the distribution o
Tools to Measure Investment Return
- Cash (Dollar) Return which measures the return in dollar value [Measures actual return in dollars]
- Rate of Return (r) which measures return as a percent return on dollar invested [Measures relative return given amount invested]
- Expected Rate of Retu
Risk is
Your likelihood of not realizing the expected return
What financial tool can you use to measure risk?
Variance in Rates of Return
Higher standard deviations ? higher risk, or higher likelihood of not realizing expected returns
It's also used to measure volatility ? how much returns fluctuated over a period
Equity risk premium
It's a way to gauge extra return to be had, given extra risk
It's the different between the return of a riskier option against a less risky option.
How much more return can be expected given the extra risk?
Volatility in US Stock vs International vs European vs Pacific stock
United States (+37.6% ; -37.0%)
International (+69.9% ; -43.1%)
European (+79.8% ; -46.1%)
Pacific (+107.5% ; -36.2%)
- The greater the difference, the more volatile the investment.
Arithmetic average return vs. geometric (or compound) average return
Aritihmentic: What was the average yearly rates of return?
Gemotric: what was the growth rate of your investment, taking compounding into account
+50% of 100 = $150, while -50% of 150 = $75 ? arithmetic average = 0%, but you ended up with $25 less than th
Compound average rate of return
Tool for measuring the affects of compounding and different returns over time on the value of an investment, given compounding, and r differences.
Geometric Average Return = [(1+ rY1) x (1+rY2) x ... etc]^(1/n) -1
Excel: same as before, solve for RATE (PV
When to choose arithmetic vs. geometric?
Arithmetic: What annual r can we expect next year?
Geometric: What annual r can we expect over a multiyear period?
Analyzing periods of different lengths using arithmetic means
You need matching periods to use arithmetic, if your studying past=1quarter, to analyze future=1year. You need to covert past to match year. You need to use geometric mean to convert the quarter into a yearly r, then analyze arithmetic
Principle 4: Market Prices Reflect Information, and stock markets
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