**Portfolio and Risk Management Quiz Answer**

### Week- 1

Graded quiz on the content of Week 1

1. A portfolio is equally split between two assets: one half of the wealth is allocated to one asset and the other half of the wealth to the other. Which of the following statements is true?

**The return of the portfolio will be the average of the returns of the two individual assets. The risk of the portfolio will be lower than the average of the two assets provided that their returns are not perfectly correlated.**- The return of the portfolio will be the average of the returns of the two individual assets. The risk will be higher than the average of the two individual assets provided that their returns are not perfectly correlated.
- The return of the portfolio will be lower than the average of the returns of the two individual assets. Same thing for the risk of the portfolio
- The return of the portfolio will be lower than the average of the returns of the two individual assets. The risk will also be lower than the average of the two individual assets provided that their returns are not perfectly correlated.

2. Complete the following sentence:

“An investor should modify his or her Strategic Asset Allocation (SAA) only if…

- …your short term views on financial markets have changed.”
- …financial markets now have different expected returns and your short term views on financial markets have changed as well.”
**…financial markets now have different expected returns.”**- …financial markets now have different expected returns or your short term views on financial markets have changed.

3. Which of the following statements regarding the correlation are true?

**The correlation is a handier tool than the covariance when trying to compare the dependence between the returns of different pairs of financial assets.****The correlation can only take value between -1 and 1.****Two variables that are perfectly correlated have a correlation equal to 1.****Two variables that are perfectly negatively correlated have a correlation equal to -1.**

4. When we want to construct portfolios, we need 3 main types of information on financial assets.

Which of the following propositions correctly describes these 3 main types of information?

- Their expected (or mean) returns, which measures the tendency of their returns.

The correlation of their returns, which measures the risk associated with these returns.

The standard deviation between the returns of the different assets, which measures the dependence between them. - The tendency of their returns, which measures the mean of these returns.

The correlation of their returns, which measures the risk associated with these returns.

The standard deviation between the returns of the different assets, which measures the dependence between them. **Their expected (or mean) returns, which measures the tendency of their returns.**

**The standard deviation of their returns, which measures the risk associated with these returns.**

**The correlation between the returns of the different assets, which measures the dependence between them.**- Their expected (or mean) returns, which measures the risk associated with these returns.

The standard deviation of their returns, which measures the tendency of their returns.

The dependence between the returns of the different assets, which measures the correlation between them.

5. Suppose the standard deviation of the returns of stock A is equal to 2%.

Which of the following statements are true?

- We don’t have enough information to compute the variance of the returns of stock A.
**We don’t have enough information to compute the expected returns of stock A.****The variance of the returns of stock A is equal to 0.04%**- The variance of Stock A can be negative.

6. Suppose a financial asset is worth $100 today. it has an expected return of 4% over 1 year and a standard deviation of 4% as well over the same time horizon. We also know that this asset’s returns are normally distributed.

Which of the following statement is true?

- In 1 year, we expect the asset to be worth $104. Moreover, there is a probability of about 99% that its price in 1 year will be between $100 and $108.
**In 1 year, we expect the asset to be worth $104. Moreover, there is a probability of about 66% that its price in 1 year will be between $100 and $108**.- In 1 year, we expect the asset to be worth $100. Moreover, there is a probability of about 66% that its price in 1 year will be between $96 and $104.
- In 1 year, we expect the asset to be worth $100. Moreover, there is a probability of about 99% that its price in 1 year will be between $96 and $104.

### Week- 2

Graded quiz on the content of Week 2

1. Asset “A” has an expected return of 6% and a volatility (or standard deviation) of 12%.

Asset “B” has an expected return of 8% and a volatility (or standard deviation) of 20%.

The correlation between assets “A” and “B” is equal to 0.6.

Which of the following statements are true?

- A portfolio that has a 75% allocation in Asset “A” and 25% in Asset “B” has a volatility of 14%.
**A portfolio that has a 75% allocation in Asset “A” and 25% in Asset “B” has a volatility of less than 14%.****A portfolio that has a 75% allocation in Asset “A” and 25% in Asset “B” has an expected return of 6.5%.**- A portfolio that has a 75% allocation in Asset “A” and 25% in Asset “B” has an expected return of less than 6.5%.

2. Which of the following statements regarding the “efficient frontier” are true?

**The upper part of the efficient frontier is the one investors should focus on since portfolios on the upper part of the frontier dominate those on the lower part.****For a given level of expected return, the portfolio that attains this level of expected return with the lowest risk must be on the efficient frontier.**- The efficient frontier can be described as the area that contains all the portfolios with the lowest risk for each level of expected return.
- The lower part of the efficient frontier is the one investors should focus on since portfolios on the lower part of the frontier dominate those on the upper part.

3. What happens when we add a risk-free asset to our investable universe?

**We are now able to build a portfolio with zero risk (i.e. certain returns).**- There is no limit to the effect of diversification anymore.
**The upper and lower parts of the efficient frontier are now two straight lines.****There is one portfolio, the tangency portfolio, which belongs to both efficient frontiers (the one with and the one without the risk-free asset).**

4. Which of the following statements regarding international diversification are true?

**International diversification is beneficial to investors’ portfolios because the returns of foreign assets are typically not perfectly correlated with those of domestic assets, but also between each other.****Global market integration can reduce the benefits of international diversification.**- Emerging markets’ equity indices generally have a high correlation with developed markets’ equity indices.
- Investors tend to invest outside of their home country more than they should.

5. You are building a portfolio for a client. You know that this investor cannot perform short sales. What does it imply?

**The fact that the investor cannot perform short sales adds a constraint to your objective of minimizing the risk of his portfolio for a given level of expected return.****The constraint this investor faces is typical for retail investors.**- The fact that the investor cannot perform short sales enhances the possibilities of diversification available to him.
**The weights (or allocation) to the different assets in this investor’s portfolio cannot be negative.**

6. Suppose an investor has access to a risk-free asset as well as many different risky securities. Which of the following statements are true?

**In the risk-return space, the investor will choose a portfolio along the line starting at the risk-free asset and going through the Tangency portfolio. The more risk averse he is, the closer his portfolio will be to the risk-free asset.****In the risk-return space, the investor will choose a portfolio along the line starting at the risk-free asset and going through the Tangency portfolio. The Tangency portfolio is the only portfolio on that line that is made up only of risky assets.**- The investor’s decision boils down to choosing an allocation between only three different portfolios: the risk-free asset, the Tangency portfolio and foreign equities.
- The investor has to choose between being fully invested in the risk-free asset or fully invested in the Tangency portfolio.

7. Suppose we are living in an economy with a risk-free asset and many different risky assets. Furthermore, all investors in the economy diversify optimally their portfolio by applying the “Minimum Variance” (or “Mean-Variance”) approach.

Which of the following statements are true?

**The Tangency portfolio becomes the market portfolio.****The market portfolio has a “beta” of 1.****The “beta” of an asset is a measure of its non-diversifiable risk.**- The return of any asset in the economy is directly (and linearly) linked to its level of diversifiable risk.

8. Suppose asset “A” has a beta of 0.7. The risk-free asset delivers a yearly return of 2%. The yearly expected return of the market portfolio is equal to 8%.

According to the Capital Asset Pricing Model (CAPM), what is the yearly expected return of asset “A”?

Please give your answer in percentage terms and round it to the nearest integer. For example, if your answer is “13.3%”, then type in “13”.

Enter answer here

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9. Which of the following statements regarding investors are true?

**Financial illiteracy can explain why many of them do not invest in the stock market.**- They often invest abroad more aggressively than what MPT would recommend.
**They often trade excessively.**- A lack of trust in the legal, financial and political institutions can explain why some investors trade excessively.

10. Which of the following statements regarding Modern Portfolio Theory (MPT) are true?

- There is clear empirical evidence that asset returns are independent over time.
- One of the assumptions of MPT is that the distribution of assets’ returns are leptokurtic.
**One of the assumptions of MPT is that investors only care about the next period and nothing beyond.****One of the assumptions of MPT is that investors invest less money in risky assets as their wealth increases**

### Week- 3

Graded quiz on the content of Week 3

1. Which of the following statements regarding the impact of age on the investment profile are true?

**When they retire, some investors get completely out of the stock market.**- Because stocks tend to offer attractive risk-adjusted returns over the short run, investors with a short investment horizon are traditionally advised to allocate a large portion of their portfolio to stocks.
- As long as they are employed, investors tend to gradually reduce their allocation to stocks as they get older.
**Because stocks tend to offer attractive risk-adjusted returns over the long run, investors with a long investment horizon are traditionally advised to allocate a large portion of their portfolio to stocks.**

2. Which of the following statements regarding the impact of wealth on the investment profile are true?

- Investors’ risk aversion is inversely related to their wealth, meaning that they become more risk averse as they get wealthier.
**Investors’ risk aversion is inversely related to their wealth, meaning that they become less risk averse as they get wealthier.****If two individuals differ only in terms of their wealth, “Robo-advisors” will tend to recommend to the wealthy individual to invest more in risky assets than the other one.**- “Robo-advisors” do not integrate wealth in their asset allocation recommendations.
- Investors’ risk aversion is positively related to their wealth, meaning that they become more risk averse as they get wealthier.

3. Which of the following actions are part of the 6 key steps of the Strategic Asset Allcoation (SAA)?

**Estimating the long run return parameters.****Defining the investor’s constraints.****Defining the investment horizon of the investor.**- Looking for undervalued securities.
- Timing the market.
**Defining the risk appetite of the investor.**

4. Which of the following statements regarding the implementation of the Strategic Asset Allocation (SAA) are true?

- Two constraints we traditionally impose on the SAA are that the portfolio weights must be positive (i.e. no leverage is allowed) and that the sum of the portfolio weights must equal 100% (i.e. no short selling is allowed).
**The “cost” of the estimation error for mean returns is a lot higher than that of variances and covariances.****Two constraints we traditionally impose on the SAA are that the portfolio weights must be positive (i.e. no short selling is allowed) and that the sum of the portfolio weights must equal 100% (i.e. no leverage is allowed).****Non-controllable market movements are the main driver behind the variation in the returns of mutual funds.****Variance and covariance estimates (that are needed for the SAA) are more precise when we use longer datasets.**- Mean returns estimates (that are needed for the SAA) are more precise when we use longer datasets.

5. Which of the following statements regarding Strategic Asset Allocation (SAA) and Tactical Asset Allocation (TAA) are true?

**The lower and upper bounds we impose on the target allocation to the different asset classes (SAA) can hinder the effectiveness of TAA if they are too tight.**- The SAA should be rebalanced as our market views evolve.
**TAA is about finding market opportunities within the ranges set by the SAA.****The SAA should be rebalanced after the assets we hold in our portfolio have experienced different levels of returns.**- No matter how high the weight allocated to bonds (with respect to stocks), one could not have escaped negative returns on his/her portfolio during the 2000-2002 bear market.

6. Which of the following statements regarding the importance of asset allocation versus stock picking are true?

**No stock in the S&P 500 index has a lower volatility than the index as a whole.**- You have to be a stock picking prodigy if you want to preserve and increase your wealth.
**By combining two asset classes, it is sometimes possible to achieve a higher return and a lower volatility than by investing solely in one of the two asset classes.****Investors that own only a few individual stocks are not properly compensated for the risk they assume in doing so.**

7. Which of the following statements regarding Tactical Asset Allocation (TAA) are true?

- Through market timing, TAA seeks to identify over- or under-valued sectors or regions.
- When a bear market is anticipated, an efficient TAA would reduce the market exposure of the portfolio by moving into risky assets.
**Market timing, valuation and the business cycle are part of the key drivers of TAA.**- TAA involves making permanent modifications to the asset allocation, either across assets or within them.
**TAA has a short to medium term horizon (i.e. from 1 month up to 1 year).**

8. What does it mean if a stock index has a high CAPE (or PE10) with respect to previous years?

**One can expect relatively low future returns for this index with respect to its historical returns over the previous years.****With respect to previous years, the aggregate earnings of the companies listed in the index are relatively low compared to the aggregate price of their shares.**- With respect to previous years, the aggregate earnings of the companies listed in the index are relatively high compared to the aggregate price of their shares.
- The aggregate earnings of the companies listed in the index have probably decreased a lot over the previous month since the CAPE (or PE10) is very sensitive to recent changes in aggregate earnings.

9. Which of the following statements regarding market timing are true?

**Switching from equities to Treasury Bills when recessions risk is high can be more profitable than a simple “Buy-and-Hold” strategy.****The US consumer confidence indicator can be used to anticipate changes in the US consumer spending and hence can be useful in predicting recessions.****Trying to time the market can result in missing some of the best days in terms of returns which can significantly hurt the performance of your portfolio.****Trying to time the market can result in missing some of the best days in terms of returns which can even translate into negative returns on your portfolio.**

10. Which of the following statements regarding Strategic Asset Allocation (SAA) and Tactical Asset Allocation (TAA) are true?

**While earnings are a very important indicator for the performance of equities, inflation is the most important one for fixed income investments.****TAA is more popular among investors and more discussed in the media than SAA, even though SAA should be everyone’s priority when building a portfolio**.- SAA is more popular among investors and more discussed in the media than TAA, even though TAA should be everyone’s priority when building a portfolio.
- While inflation is very important indicator for the performance of equities, earnings are the most important one for fixed income investments.

### Week- 4

Graded quiz on the content of Week 4

1. Which of these positions in derivative instruments have a payoff profile at maturity that is a linear function of the price of their underlying asset?

**Being short a forward**- Being short a put option.
**Being long a forward.**- Being long a call option.
- Being long a put option.
- Being short a call option.

2. Which of the following statements regarding the OTC (Over-The-Counter) trading of derivative contracts are true?

**Derivative contracts traded OTC are “tailor-made” and primarily issued by banks and insurance companies.****Derivative contracts traded OTC are subject to counterparty risk.**- Derivative contracts traded OTC are standardized to improve their liquidity.
**In terms of notional value, derivative contracts traded OTC represent the largest part of the total volume of derivative trading.**

3. Mary is short a call option written on Stock A with a strike price of $65. The price of Stock A is currently $55.

Which of the following statements are true?

- Mary’s position has an unlimited potential gain and a limited potential loss.
**Mary’s position has a limited potential gain and an unlimited potential loss.****Mary received a premium when she entered this derivative contract.**- Mary had to pay a premium when she entered this derivative contract.

4. Which of the following statements regarding volatility as a risk measure for a portfolio are true?

**It implicitly assumes that the distribution of returns of the portfolio is symmetric, i.e. that profits and losses are mirror images of each other.****It is not an appropriate risk measure for a portfolio made of options.****When faced with asymmetric return distributions, it is important to focus on large potential losses.**- It is an appropriate risk measure for a portfolio made of options.

5. What are the values of letters A to G?

- A = 1300

B = 30%

C = 400

D = 33.33%

E = 0.4

F = 33.33%

G = 3.33% - A = 1200

B = 20%

C = 400

D = 33.33%

E = 0.4

F = -33.33%

G = -3.33% **A = 1300**

**B = 30%**

**C = 520**

**D = 73.33%**

**E = 0.4**

**F = 33.33%**

**G = 43.33%**- A = 1300

B = 30%

C = 520

D = 33.33%

E = 0.4

F = 33.33%

G = -3.33%

6. Which of the following statements regarding currency risk are true?

- The dominant risk in foreign equity investments is currency risk.
- The dominant risk in foreign bond investments is local asset return volatility.
**Currency risk can sometimes benefit investors that invest abroad.**- The dominant risk in foreign equity investments is local asset return volatility.
**The dominant risk in foreign bond investments is currency risk.**

7. The Value-at-risk (VaR) with a confidence level of 99% is a measure of risk that is the answer to one of the following questions. Which one?

- What is the probability level such that there is a chance of 99% to observe a larger loss?
- What is the loss level such that there is a probability of 99% to observe a larger loss?
- What is the probability level such that there is a chance of 1% to observe a larger loss?
**What is the loss level such that there is a probability of 1% to observe a larger loss?**

8. The Expected Shortfall (ES) is a measure of risk that is the answer to one of the following questions. Which one?

- What is the maximum loss, knowing that the loss is below the Value-at-risk (VaR)?
**What is the average loss, knowing that the loss is above the Value-at-risk (VaR)?**- What is the average loss, knowing that the loss is below the Value-at-risk (VaR)?
- What is the maximum loss, knowing that the loss is above the Value-at-risk (VaR)?

9. Which of the following statements regarding the portfolio indicated by the blue star in this graph are true?

- The portfolio is optimally diversified.
**The portfolio is not optimally diversified.****The portfolio satisfies the 95% VaR constraint.**- The portfolio does not satisfy the 95% VaR constraint.

10. An investor has invested in Stock A. This investor has hedged herself against a drop in the price of Stock using a put option.

Which of the following statements are true?

- The investor cannot benefit anymore from an increase in the price of Stock A.
- The investor is short the put option.
**The investor had to pay a premium to hedge herself using the put option.****The investor can still benefit from an increase in the price of Stock A.****The investor is long the put option.**- The investor received a premium to hedge herself using the put option.