Lesson 2 of Investment Planning: Portfolio Theory Flashcards
Standard Deviation!
-
Standard Deviation is
- a measure of risk and variable of returns.
- The higher the standard deviation, the higher the riskiness of the investment.
- SD in simple terms, measures how much something flip-flops around on average.
- SD can be used to determine the total risk of an undiversified portfolio.
- For CFP EXAM be prepared to:
- Use SD to determine the profitability of returns.
- Calculate the SD.
SD to Calculate a Probability of Returns
The graph below illustrates a normal distribution with probabilities between +/- 1, 2, and 3 standard deviations away from the average.
EXAM TIP
Memorize the 68, 95 & 99 depending if the returns are +/- 1, 2, or 3 SD sway from the average.
Example of SD to Calculate Profitability of Returns
Calculating SD with a Financial Calculator
- The first thing you do is click 2nd and then click 7 for (data)
- Second you click 2nd and then click CE/C for (CLR Work).
- The type of inputs into the calculator. Make sure X01,2,3… is what the information is being put into. Click the down arrow to navigate between the X0’s. Click enter after input is in each time you input a number in, and then click the down arrow.
- Y01 should be left as is. Should be 1. Skip to the next X0.
- When all numbers are in click 2nd and then click 8 for (stat).
- Scroll down until you see 1-V. When you find that, press enter.
- After you press the down arrow and you should see all the stats associated.
- SD = Sx
X with the line above is the mean.
https://www.youtube.com/watch?v=l1jo6CpYATA
Calculating SD with a Financial Calculator
Exam Tip
It is possible that a CFP Exam Question regarding SD could simply be “ Which of the following assets is most risky?” They are really asking you to calculate SD and select the asset with the HIGHEST standard deviation.
2nd way to calculate standard deviation
- The examiners may provide you with the expected returns for a stock or fund with the likelihood (probability that those returns will be realized.
- The calculation is simply the sum of all expected returns multiplied by their respective probabilities
- Expected Return = Σ (Return x Probability)
Example of 2nd way to calculate standard deviation
Shantele has been looking at mutual funds and her advisors tells her about a great fund with the following expected returns and probability of obtaining each return.
Expected Return:
10%
15%
18%
Probability of Returns:
30%
60%
10%
Answer:
The total expected return is 13.8%
= (10% x 30%) + (15% x 60%) + (18% + 10%)
Coefficient of Variation!
- The coefficient of variation is useful in
- determining which investment has more relative risk
- when investments have different average returns.
- Useful when comparing two assets with different average returns.
- The coefficient of variation tells us the
- probability of actually experiencing a return close to the average return.
- The higher the coefficient of variation the more risky
- an investment per unit of return.
The formula for the Coefficient of Variation
Not given on exam
CV = Standard Deviation ÷ Average Return
Example of CV
Example 1:
Which one is more risky?
Stock A: SD = 12% and Average Return = 8%
Stock B: SD = 10% and Average Return = 8%
The coefficient of variation is not necessary to determine which investment is more risky because their average returns are the same. Stock A is more risky because it has the same return, but a higher SD.
Example 2:
Alternatively, if Fred had the following investment opportunities, which one has the highest risk per unit of return earned?
Stock A: SD = 12% and Average Return = 10%
Stock B: SD =8% and Average Return = 5%
Stock A: CV = 0.12 ÷ 0.10 = 1.2
Stock B: CV = 0.08 ÷ 0.05 = 1.6
Therefore, Stock B has more risk per unit of return compared to A. You cannot assume that because Stock A has a higher standard deviation that is has a higher adjusted return.
Could ask which has a higher risk adjusted return which would be lower CV.
Distribution of Returns!
- Normal Distribution
- Lognormal Distributions
- Skewness
Normal Distribution
- A normal distribution is appropriate if an investor is considering a range of investment returns, as was covered above.
Logonormal Distribution
- A lognormal distribution is not a normal distribution.
- A lognormal distribution is appropriate if an investor is considering a dollar amount or portfolio value at a point in time.
For example:
- If an investor invests $1 into the market 60 years ago, it would be worth $60 today. With a lognormal distribition you are looking for a trend line or ending dollar amount.
Skewness
- Skewness refers to a normal distribution curve shifted to the left or right of the mean return.
- Commodity returns tend to be skewed.
- A distribution is positively skewed when
- its tail is more pronounced on the right side than it is on the left.
- Since the distribution is positive, the assumption is that its value is positive.
- As such, most of the values end up being left of the mean.
- This means that the most extreme values are on the right side.
- In statistics, a negatively skewed (also known as left-skewed) distribution is a type of distribution in which
- more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
Kurtosis
- Kurtosis refers to variation of returns. If there is little variation in returns, the distribution will have a high peak.
- Treasuries have little variation of returns, have a high peak, and, therefore, have a positive kurtosis.
- If returns are widely dispersed, the peak of the curve will be low and have a negative kurtosis.
- Leptokurtic = High peak and fat tails (higher chance of extreme events)
- Platykurtic = Low peak and thin tails (lower chance of extreme events)
Exam Tip
- Leptokurtic = High peak and fat tails (higher chance of extreme events)
- Platykurtic = Low peak and thin tails (lower chance of extreme events)
**OTHER: **
- In statistical terms, “fatter tails” refer to the relatively higher probability of extreme or outlier events in a distribution.
- Tails in a distribution represent the regions of values that are far from the mean (average).
- A distribution with fatter tails has a higher likelihood of observing values at a greater distance from the mean compared to a distribution with thinner tails.
Exam Question
Conrad has noticed that the stock she purchased tends to have a very high tight distribution around the mean but there seems to be a high probability of “outliers” (multi-deviation returns). This is most indicative of what type of curve?
a) Positive skewness
b) Leptokurtosis
c) Normal
d) Lognormal
Answer: B
The leptokurtic distribution reflects the tendency of observations to fall closely around the mean creating a peaked distribution at the mean with thicker tails. If historical returns indicate leptokurtosis then there is much more reserved variation in periodic returns but a higher probability of large multi-sigma deviations (i.ie “fat tails”)
Mean-Variance Optimization
Mean-variance optimization is the process of
- adding risky securities to a portfolio but
- keeping the expected returns the same.
- It’s finding the balance of combining asset classes that
- provide the lowest variance as measured by standard deviation.
Monte Carlo Simulation
- Monte Carlo Simulation is a spreadsheet simulation that gives a probabilistic distribution of events occurring.
- For example, what is the probability of running out of money in retirement with a client who has a withdrawal rate of 3%, 4%, or 5%.
- Monte Carlo simulation then adjusts assumptions and returns the probability of an event occurring depending upon the assumption.
- Allows for “what if” scenarios and sensitivity analysis if variables such as inflation or savings rate change.
Exam Tip
It’s not likely that the above concepts will be tested. Know the characteristics.
If there is a question it will most likely be to adjust the assumptions.
Covariance!
Covariance is the measure of
- two securities combined and their interactive risk.
- In other words, how price movements between two securities are related to each other.
Covariance is a measure of relative risk.
- If the correlation is known, or a given, covariance is calculated as
- the deviation of investment ‘A’ times the deviation of investment ‘B’ times the correlation of investment ‘A” to investment ‘B’, thus:
Covariance Formula