Lesson 5

Question 1

5.1.1 Assume you’re considering to assess for your portfolio:

A risk free T-bill and a stock the expected return is 3% on the T-Bill and 10% on the stock.

The standard deviation of the stock is 20%.

Compare the expected return and risk as measured by standard deviation if you put 100% of your portfolio in the stock as compared to the T-Bill

Answer 1

The T-bill will have a return of 3% and or risk of 0%

Investing 100% in the stock would give you an expected return on your portfolio of 10% in a portfolio risk of 20%

Question 2

5.1.2 Assume you’re considering to assess for your portfolio a risk free T Bill and a stock.

The expected return is 3% on the T-Bill and 10% on the stock.

The standard deviation of the stock is 20%.

Calculate the expected return and standard deviation of your complete portfolio if you allocate 25% of the table and 75% to the stock and explain the trade off

Answer 2

The expected return using to complete portfolio formula will be 8.25%. The standard deviation of the complete portfolio will be 15%.

As expected both the expected return and the standard deviation or higher than those of the T-Bills alone in lower than those for the stock alone

Question 3

5.1.3 Your risky portfolio has an expected return of 10% and a standard deviation of 20%. The risk-free rate is 6%. Calculate expected return on your complete portfolio if you:

A) allocate 80% to the risky portfolio
B) allocate 60% to the risky portfolio

Explain the trade off in your expected return to the two scenarios

Answer 3

A) 9.2%
B) 8.4%

Shifting a greater proportion to the lower in return risk free assets reduces the return on the complete portfolio but also reduces the risk NBC

Question 4

5.1.4 I assume you’re considering to assess for your portfolio: a risk free T-Bill and a stock.

The expected return is 3% on the T-Bill and 10% on the stock. The standard deviation of the stock is 20% you have two options:

1. Allocate 80% of the risky portfolio
2. Allocate 60% of the receipt portfolio

Explain the the risk trade off between the two scenarios

Answer 4

The standard deviation of the complete portfolio is the standard deviation of the risky asset multiplied by the weight of the risk asset in that portfolio.

1. The standard deviation of the 80% allocation is 16%
2. The standard deviation of the 60% allocation is 12%

Shifting in greater proportion to the lower return risk-free asset reduces the risk; however it will also reduce the expected return

Question 5

5.2.1 Define capital allocation line (CAL) and explain its purpose

Answer 5

The capital allocation line shows the expected return and the risk as measured by standard deviation of every single combination of risk-free and risky assets available to an investor for a capital allocation.

Expected returns are plotted on the Y axis and standard deviation is on the X axis. The capital allocation line aids investors and choosing how much to invest in a risk-free assets and one or more risky assets.

The slope measures the trade off between the risk and return and equals the increase in the expected return of the chosen portfolio per unit of additional standard deviation. A steeper slope means that investors receive higher expected returns in exchange for taking on more risk

Question 6

5.2.2 Interpret the following capital allocation line

a) risk free rate
b) what is the slope

Answer 6

1. This CAL is plotted assuming the risk-free rate is 4% and it’s standard deviation is 0
2. The riskiest asset on the CAL has an expected return of just under 12% and the standard deviation of 15%
3. The difference between the risk-free rate and any given standard deviation along the line is the risk premium expected by the investor for that risk return combination
4. Increasing the fraction of the overall portfolio invested in risky assets increases expected return and standard deviation
5. The slope of the CAL is known as the reward to variability ratio or the sharpe ratio
6. The CAL illustrates the investment opportunities set available to investors

Question 7

5.2.3 Explain how individual differences in risk aversion affect capital allocation choices when investors are choosing from an identical investment opportunity set as depicted by the CAL

Answer 7

The CAL provides a graph of all feasible risk return combinations available for capital allocation.

The investor can use the EAL to choose one of the more combination trading off risk and return. The investors choice will depend on their level of risk aversion

Question 8

5.3.1 Assume your risk aversion index is three, the rate of return on your risk free portfolio is 7%. The rate of return on your risky portfolio is 15% and it’s standard deviation is 22%. Determine your optimal portfolio of risky and risk-free assets

Answer 8

You would choose the allocation to the risky asset that maximizes your utility function. Giving your risk aversion index and return characteristics of your options your optimal portfolio is 55% risky assets and 45% risk free assets

Question 9

5.3.2 Assume your risk aversion index is three, the rate of return on your risk-free portfolio is 7% the rate of return on your whiskey portfolio is 15% it’s standard deviation is 22% and your optimal portfolio allocation to risky asset is 55%.

Calculate the expected return and identify standard deviation on your optimal portfolio

Answer 9

The standard deviation is 12.1% and the expected return is 11.4%

Question 10

5.3.3 Assume your risk aversion index is 6, the rate of return on your risk free portfolio is 7%, the rate of return on your risky portfolio is 15% and it’s standard deviation is 22%. Determine the change in your optimal portfolio and risky and risk-free assets

Answer 10

Your optimal portfolio is a combination of 27.5% risky assets and 72.5% risk free assets

Question 11

5.3.4

Answer 11

Information that can be interpreted from this craft includes:

1. Each curve connects investment portfolios with the same utility level
2. Utility levels are affected by the investors index of risk aversion
3. Portfolios on steeper indifference curves offer a higher expected return for any given squabble
4. Higher in difference curves correspond to higher levels of utility
5. Investors with a high risk tolerance require the same expected return incentive to except more portfolio risk
6. As risk aversion increases investors demand more return for each unit of increase in risk
7. When risk increases investors demand more return based on the utility function there by keeping the level of utility the same

Question 12

5.4.1 Briefly describe a passive investment strategy

Answer 12

With a passive investment strategy, there is no direct or indirect security analysis. Investors do not require information on any individual stock or group of stocks. A passive strategy involves investing in to portfolios, virtually risk-free short term T-bills and I diversified portfolio frisky assets

Question 13

5.4.2 Explain the relationship between the capital market line [CML] and passive investment strategy

Answer 13

CML is the capital allocation line that represents a passive investment strategy comprising virtually risk free, short term T-bills and a fund of common stock that mimics a broad market index

Question 14

5.4.3 Compare the cost and benefits of an active investment strategy with a passive investment strategy

Answer 14

Constructing an active portfolio is more expensive than constructing a passive one

After portfolios require an investment of time and money by the individual investor to acquire the information needed to generate an optimal after portfolio or delegating that task to a professional. Either way there’s a cost.

Passive strategies also reflect the free rider benefit. If we assume there are many active knowledgeable investors quickly bidding on prices of undervalued assets and bidding down overvalued assets we can conclude that most stocks are fairly priced. Therefore a well diversified portfolio of common stock may be reasonably fair to buy

Question 15

5.5.1 Define diversification and briefly Outline its role in portfolio construction

Answer 15

Diversification is the process of spreading funds available for investment across assets.

Diversification across many assets will eliminate some of the risk associated with individual assets with the idea that good performance will outweigh poor performance between assets

In constructing a portfolio investors to determine how much risk they are willing to take on and then they can allocate or diversify their portfolios according to the results of that decision

Question 16

5.5.2 Contrast systemic risk with non-systemic risk

List three sources of systemic risk

Answer 16

Systemic risks are characteristic of entire market, a specific asset class or a portfolio investment in the asset class. Systemic risk is also called market risk or nondiversifiable risk.

Sources of systemic risk include country risk, political risk, and inflation risk.

Non-systemic risk is diversifiable , which means the rest can be reduced by proper diversification. When our risk is non-systemic diversification can reduce risk to arbitrarily low levels

Question 17

5.5.3 Explain how the law of diminishing returns in packs diversification in a portfolio

Answer 17

Risk reduction from adding securities drops off as more and more securities are added to a portfolio.

With 10 securities most of the diversification affect is already realized and with 30 or so there is very little remaining benefit.

The benefit of further diversification increases at a decreasing rate, the law of diminishing returns applies.

It is an application of the principle that a continual increase in effort or investment does not lead to continue increase in output or results

Question 18

5.6.1 Define correlation and explain how correlation coefficient are interpreted

Answer 18

Correlation is a statistical concept using determining the degree of similarity between two random variables.

It is used to determine the extent to which the returns on to assets move together. Correlation between variables is translated into a value known as the correlation coefficient.

The correlation coefficient value falls between the range of -1 and 1

Question 19

5.6.2.a Explain what a graph might look like for two equities with a correlation coefficient of one, zero, and -1

Answer 19

1. A correlation of one indicates that the two assets of perfect positive correlation. Whenever asset A realizes up or down asset B moves in lockstep in the same direction so the points in the graph would be in a straight line with a slope of one.
2. A correlation coefficient of zero indicates that the two assets are perfectly unrelated and would have a graph with scattered points points. The movement of asset A indicates nothing about the movement of asset B
   - 1. A correlation coefficient of negative one with indicating that the assets of a perfect negative correlation so asset A and Asset B would move in lockstep in opposite directions and the graph would have a line of points with the slope of -1

Question 20

5.6.3 Describe the diversification benefits of adding either two highly correlated assets or two negatively correlated assets to a portfolio

Answer 20

Combining two highly correlated assets offers limited diversification benefit. The two assets will move together

However if two assets are negatively correlated, whenever in return on one goes up the other tends to go down. For two assets that are negatively correlated, there will be substantial diversification benefit because variation on the return on one asset tends to be offset by variation in the opposite direction on the other. If two assets have a perfect negative correlation combining them eliminates all risk. Perfect negative correlation is mostly only found in synthetic financial instruments such as futures contracts

Question 21

5.6.4 Explain how covariance is interpreted. What do positive and negative covariance indicate And which is preferable for diversification.

Answer 21

Covariance is a measure of the extent or degree to which returns on too risky assets change in tandem.

Positive covariance indicates that higher than average values of one variable tend to be paired with higher than average values of the other variable.

Negative covariance indicates that higher than average values of one variable tend to be paired with lower than average values of another very well.

Holding assets that provide returns that have a high covariance with each other does not provide very much diversification. Greater diversification can be achieved by investing in assets that have a local variance to each other

Question 22

5.7.1

Answer 22

Beyond a certain point adding more of the lower risk bond fund actually increases your risk. As the bond and the stock have a low correlation and will give you diversification benefits. You can achieve a higher expected return and lower standard deviation by investing in both stocks and bonds

Question 23

5.7.2

Answer 23

Each of the points on the graph represents a possible combination of a risk and return available from a portfolio bonds and stocks. As expected returns increase, risk increases. The portfolio that has the smallest standard deviation is the minimum variance portfolio

Any portfolio that plots below the minimum variance portfolio is a poor choice, because no matter which one you pick there is another portfolio with the same rest and a much better return. Given the level of risk the expected return is in adequate compared with some other portfolios of equivalent risk.

Question 24

5.7.2.b Define efficient portfolio

Answer 24

A portfolio that offers the highest return for its level of rest is said to be in efficient portfolio. On a minimum variance portfolio grab the minimum variance portfolio and all the portfolios a plied above that are considered efficient

Question 25

5.8.1.a Describe the Markowitz efficient frontier

Answer 25

The Markowitz efficient frontier assumes that an investor wants to maximize our portfolios expected return contingent on any given amount of risk, with the rest measured by the standard deviation of the portfolios rate of return. It is the set of portfolios with the maximum Return forgiven standard deviation

Question 26

5.8.1.b Explain the importance of risk and expected return trade off in applying the Markowitz efficient frontier

Answer 26

For portfolios that satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation, efficient frontier portfolios, achieving a higher expected return requires taking on more risk.

So investors are faced with a trade off between risk and return. This means that individual investors should determine how much rest they’re willing to take on, and then they can allocate or diversify their portfolios according to the results of that decision

Question 27

5.8.2

Answer 27

Portfolios that comprised of the efficient frontier tend to have a higher degree of diversification than suboptimal ones, which are typically less diversified

Portfolios that lie below the efficient frontier are sub optimal they do not provide enough return for that level of risk.

Portfolios the cluster to the right of the efficient frontier are sub optimal they have a higher risk for the expected rate of return

Question 28

5.8.3 Explain the limitations of the Markowitz efficient frontier

Answer 28

The Markowitz efficient frontier assumes that the asset returns follow a normal distribution.

However securities may experience returns that are abnormally distributed. The theory also assumes investors are rational and avoid risk when possible, there are not large enough investors to influence market prices, and investors have unlimited access to borrowing and lending money at risk free interest rate.

However the market includes irrational and risk seeking investors, large market participants who could influence market prices investors who do not have unlimited access to borrowing and lending money. The Markowitz efficient frontier assumes all investors have the same expectations