Week 6 Everything Flashcards
The expected cash flow
The expected cash flow is the weighted average of the possible cash flows outcomes such that the weights are the probabilities of the occurrence of the various states of the economy.
Expected Cash flow (X)
(X) = ΣPbi*CFi
Where Pbi = probabilities of outcome i
CFi = cash flows in outcome i
Holding-period return
payoff during the “holding” period.
Holding period could be any unit of time such as one day, few weeks or few years.
Holding period gain =
Price end of period + cash distribution (dividend) - price beginning of period
Expected Return example
You bought 1 share of Google for $524.05 on April 17 and sold it one week later for $565.06. Assuming no dividends were paid, your dollar gain was:
565.06 – 524.05 = $41.01
Therefore, Google rate of return:
41.01/524.05 = .0783 or 7.83%
Measuring the Expected Return example 2
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Expected Rate of Return
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Risk involvement to the Expected Rate of Return
Three important questions:
What is risk?
How do we measure risk?
Will diversification reduce the risk of portfolio?
Definition of Risk
Risk is the possibility of actual outcome deviating from what is expected. In the finance world, risk is linked to possibility of unexpected fluctuation in security prices, possibility of expected cashflow to materialize or possibility of achieving expected returns. Generally speaking, high levels of risk are associated with high potential returns. Commercially, risk types can be strategic, financial, legal, regulatory and operational risk. These may be individually assessed or as a combination.
How can risk be measured
Risk refers to potential variability in future cash flows. The wider the range of possible future events that can occur, the greater the risk. Thus, the returns on common stock are more risky than returns from investing in a savings account in a bank. Risk can be measured as variability of actual returns from expected returns. Some common measures of risk are standard deviation and systematic risk.
Consider two investment options:
Invest in Treasury bond that offers a 2% annual return.
Invest in stock of a local publishing company with an expected return of 14% based on the payoffs (given on next slide).
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Treasury bond = 12% = 2%
Stock
= 0.1-10 + 0.25% + 0.415% + 0.225% + 0.130%
= 14%
We observe from above that the stock of the publishing company is more risky but it also offers the potential of a higher payoff.
Standard deviation (S.D.) is one way to measure risk.
Standard deviation (S.D.) is one way to measure risk. It measures the volatility or riskiness of portfolio returns.
S.D.
square root of the weighted average squared deviation of each possible return from the expected return.
STANDARD DEVIATION
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Five –step Procedure standard deviation
Step 1
Calculate the expected rate return of the investment, which was calculated previously to be 14 percent.
Five –step Procedure standard deviation
Step 2
Subtract the expected rate of return of 14 percent from each of the possible rates of return and square the difference.
Five –step Procedure standard deviation
Step 3
Multiply the squared differences calculated in step 2 by the probability that those outcomes will occur.
Five –step Procedure standard deviation
Step 4
Sum all the values calculated in step 3 together. The sum is the variance of distribution of possible rate of return. Note that the variance is actually the average squared difference between the possible rates of return and the expected rate of return.
Five –step Procedure standard deviation
Step 5
Take the square root of the variance calculated in step 4 to calculate the standard deviation of the distribution of possible rates of return.
Five –step Procedure standard deviation example
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How to interpret standard deviation as a measure risk?
The greater the standard deviation, greater is the variance between each return and the mean, indicating a greater risk. Blue chip vs speculative?
For a normal distribution of data …
- 26% probability, actual data within 1 standard deviation of the mean.
- 44% probability, actual data within 2 standard deviations of the mean.
- 74% probability, actual data within 3 standard deviations of the mean.
Comments on S.D.
There is a 68.27% probability that the actual returns will fall between 2.86% and 25.14% (= 14% 11.14%). So actual returns are far from certain!
Risk is relative; to judge whether 11.14% is high or low risk, we need to compare the S.D. of this stock to the S.D. of other investment alternatives.
To get the full picture, we need to consider not only the S.D. but also the expected return.
The choice of a particular investment depends on the investor’s attitude toward risk.