Chapter 15 - Managing Your Client's Investment Risk - 5%

Question 1

What are the differences between Historical Risk, Expected Risk and Realized Risk?

Answer 1

Historical Risk measures describes the actual risk experienced by an investment in a past time period.

An investment’s expected risk on the other hand is an individual’s or firm’s estimate of what the investment’s risk will be over some future time period.

Realized risk is the risk exhibited by the investment over some historical time period. Just a past returns are never a guarantee of future returns, historical risk should not be considered a perfect indicator of expected risk.

Question 2

What is standard deviation of returns?

Answer 2

The standard deviation of returns or just standard deviation, measures the extent to which investment returns differ from the average return (in the case of historical standard deviation) or expected return (in the case of standard deviation). It measures the total risk of a security or portfolio.

Standard deviation of Historical Returns
(please refer to page 15.9 in the textbook for formula)

Question 3

What is Beta?

Answer 3

Beta is a measure of the systematic risk of an investment. Beta is usually calculated for equity securities or a portfolio of equity securities, such as an equity mutual fund. Beta is a measure of the relative risk of a security compared to the risk of the overall market, which is usually taken to be a broad market index of securities. By definition, the index has a beta of 1. Thus securities, with a beta greater than 1 have more systematic risk than the market, and securities with a beta less than 1 have less systematic risk than the market.

Question 4

Explain diversification and correlation.

Answer 4

The risk of a portfolio of securities depends not only on the risk of the individual securities, but also on the correlation coefficient of each pair of securities return.

The correlation coefficient between two securities measures the strength of the relationship between their returns. That is, it is a measure of the degree to which the securities’ returns deviate from their expected return at the same time. The correlation coefficient can have a value between or equal to +1 and -1.

Question 5

Explain the different Options.

Answer 5

Long Call Option: Right to buy the stock.
Long Put Option: Right to sell the stock.
Short Call Option: Obligated to sell the stock, if called upon to do so.
Short Put Option: Obligated to buy the stock, if called upon to do so.

Question 6

How do you calculate the number of contracts, when buying a protective put on a stock portfolio?

Answer 6

No. of contracts =

Value of Portfolio X Portfolio Beta) /
(Current Index Value X Contract Multiplier

Question 7

What are collars?

Answer 7

Collars have grown in popularity as a hedging vehicle probably because they provide all the protection offered by a protection put, but usually do so without requiring any cash outlay. Collars are used by investors who want to reduce the downside risk of an equity position, and who in order to obtain this protection are willing to forgo some of the stock’s upside potential. Investors construct a collar by purchasing an out-of-the-money put while simultaneously writing an out-of-the-money call.

Question 8

How can using futures contracts reduce risk?

Answer 8

A futures contract is a legally binding agreement traded on a regulated futures exchange. All futures contracts have a buyer and a seller and an expiration date. The buyer of a futures contract promises to take delivery of a specified amount of an underlying asset on a certain date in the future at an agreed upon price (entry price/delivery price); the seller promises to make delivery of the asset on the same terms.
The initial value of a futures contract to both buyer and seller is zero. The contract only gains value as the futures price changes. If the futures price goes up, the value of the long position goes up and the value of a short position goes down and vice-versa. There is no cost to enter into a futures position, however the buyer and seller must deposit and maintain margin in their futures accounts.
There are two level of margin that are used in futures trading – original and maintenance margins. Original or initial margin represents the required deposit when a futures contract is entered into. Maintenance margin is the minimum balance for margin required during the life of the contract.

Question 9

Wadi anticipates a drop of 100 points in the S&P/TSX 60 Index and wants to protect a $400,000 portfolio of blue-chip Canadian stocks using S&P/TSX 60 Index at-the-money put options. A historical analysis reveals that the portfolio has a beta of 1.3 relative to the S&P/TSX 60 Index (current level of the index is 760). How many put option contracts should Wadi purchase to protect his portfolio from a potential loss, and what is the potential loss to his portfolio?
A. 5 put option contracts, and a potential loss of 13.16%.
B. 5 put option contracts, and a potential loss of 17.11%.
C. 7 put option contracts, and a potential loss of 13.16%.
D. 7 put option contracts, and a potential loss of 17.11%.

Answer 9

D is correct.

Wadi should purchase 7 put option contracts to protect his portfolio from a potential loss of 17.11%. Once the beta has been determined, use the following formula to determine the number of contracts to use:

Number of Contracts = Value of Portfolio × Portfolio Beta/Current Index Value × Contract Multiplier = (4000001.3)/(760100) = 6.84 (7 contracts)

A beta of 1.3 relative to the S&P/TSX 60 Index means that for every 1% change in the level of the index, the portfolio is expected to change by 1.3%. In this case a drop of 100 in the level of the index means a drop of 13.16% in the index, which translates to a 17.11% loss in the portfolio.

Question 10

What portion of a security’s total risk is related to fluctuations in the return on the overall market?
A.	Non-systematic risk.		 	 
B.	Unique risk.		 	 
C.	Diversifiable risk.		 	 
D.	Systematic risk.

Answer 10

D is correct.

Systematic risk, or market risk, refers to the portion of a security or portfolio’s total risk that is related to fluctuations in the return on the overall market. Unsystematic risk refers to the portion of a security or portfolio’s total risk that is not related to fluctuations in the overall market.

Question 11

Which statement about various financial products or strategies is incorrect?
A. Derivatives may be used to reduce the systematic risk of a portfolio.
B. Diversification may be used to reduce the market risk of a portfolio.
C. The in-the-money portion of a call or put option is known as the option’s intrinsic value.
D. Index options can usually be exercised only at the expiration date.

Answer 11

B is correct.

Diversification may not be used to reduce the market risk of a portfolio. Rather, diversification is used to reduce the unsystematic (non-market) risk of a portfolio.

Question 12

Alex owns 1000 shares of ACZ. He purchases 10 $60 ACZ puts at $2 and writes 10 $65 ACZ calls also with a $2 premium. ACZ shares are currently trading at $62, and both calls and puts expire in 60 days. Which statement about the value of Alex’s position in relation to the price of ACZ shares at option expiration is correct?

A. If the price of ACZ shares at option expiration is $55, Alex’s call options position will be worth $10 per share.

B. If the price of ACZ shares at option expiration is $55, Alex’s put options position will be worth $10 per share.

C. If the price of ACZ shares at option expiration is $70, the value of Alex’s collared stock position will be $70 per share.

D. If the price of ACZ shares at option expiration is $70, the value of Alex’s collared stock position will be $65 per share.

Answer 12

D is correct.

If the price of ACZ shares at option expiration is $70, the value of Alex’s collared stock position will be $65 per share.

By writing the $65 calls, Alex has limited the upside potential to $3 per share (and the value of his collared stock position to $65 per share). If the stock price at option expiration goes down to $55, each of Alex’s puts will be worth $5 and each of his calls, $0.

Question 13

Which statement about futures contracts is correct?
A. In a futures contract, the buyer has the option to buy a specified amount of an underlying asset from the seller.
B. Futures contracts are sold at a premium.
C. The seller or buyer of a futures contract may offset his position by entering into an offsetting transaction in the same futures contract.
D. The number of futures contracts an investor should use to hedge a particular portfolio is one.

Answer 13

The seller or buyer of a futures contract may offset his position by entering into an offsetting transaction in the same futures contract. Either the seller or the buyer, or both, can offset his position by entering into an offsetting transaction in the same futures contract. The profit or loss when a position is offset equals the difference between the offset price and the original entry price.

Question 14

What does standard deviation measure?
A. The normal distribution of an investment.
B. The total risk of an investment.
C. The systematic risk of an investment.
D. The strength of the relationship between two securities.

Answer 14

Standard deviation measures the extent to which investment returns differ from the average return or expected return. Standard deviation measures the total risk of a security or portfolio.

Question 15

If the monthly standard deviation of a stock is 2%, what is the stock’s annualized standard deviation?
A.	0.17%		 
B.	2%		 	 
C.	3.5%		 	 
D.	6.93%

Answer 15

2% × the square root of 12 = 2% × 3.4641 = 6.9282% (rounded to 6.93%)

Question 16

When is a put option considered to be in-the-money?
A. If the strike price of the put is greater than the market price of the underlying asset.
B. If the market price of the underlying asset is greater than the strike price of the put.
C. If the market price of the underlying asset is equal to the strike price of the put.
D. If the intrinsic value of the put option is zero.

Answer 16

A is correct.

A put option is considered in-the-money when the market price of the underlying asset is lower than the option’s strike price. The in-the-money portion of a call or put option is known as the option’s intrinsic value.

Question 17

Theoretically, what optimal value of the correlation coefficient between securities maximizes the benefits of diversification?
A.	+1		 	 
B.	0.5		 	 
C.	0		 	 
D.	-1

Answer 17

D is correct.

The correlation coefficient between two securities measures the strength of the relationship between their returns. Diversification benefits result when securities that are less than perfectly positively correlated are combined in a portfolio. The ultimate in diversification comes when securities are perfectly negatively correlated, that is, when their correlation coefficient is equal to -1.0.

Question 18

What hedging strategy would be most suitable for a client who has bought a stock and would like to limit her downside risk?
A.	Buy a call.		 	 
B.	Buy a put.		 
C.	Sell a call.		 	 
D.	Sell a put.

Answer 18

B is correct.

A protective put consists of a long position in an underlying asset and a long put option on the underlying asset. Protective puts may be purchased when the stock is purchased or at any time afterwards. The long put gives its holder the right to sell the underlying stock at a fixed price on or before the expiration date. This right sets a minimum sale price for the investor’s stock position over the life of the option, no matter how low the stock price falls.

Question 19

If returns are normally distributed, approximately what percentage of all returns lie within 2 standard deviations of the average or expected return?
A.	68%		 	 
B.	99%		 	 
C.	82%		 	 
D.	95%

Answer 19

If returns are normally distributed then approximately 95% of all returns lie within two standard deviations of the average or expected return.

Question 20

Securities A and B have a correlation of +0.7. What will the relationship most likely be between the returns on Security A and Security B?
A. When Security A’s return is positive, Security B’s return will be negative.
B. When Security B’s return is positive, Security A’s return will be negative.
C. When Security A’s return is positive, Security B’s return will be positive.
D. The returns of Securities A and B are independent.

Answer 20

C is correct.

When Security A’s return is positive, Security B’s return will be positive. When two securities have positive correlation, a positive return on one security is usually accompanied by a positive return on the other. The closer the correlation is to +1.0, the more likely it is that the returns will both be either positive or negative during any given period.

Question 21

Which statement about diversification is correct?
A. Ultimate diversification occurs when securities are perfectly positively correlated.
B. “Diworsification” occurs when securities are perfectly negatively correlated.
C. A client should add securities to her portfolio regardless of the cost of maintaining the portfolio.
D. Diversification yields benefits when securities that are less than perfectly positively correlated are combined in a portfolio.

Answer 21

D is correct.

Diversification yields benefits when securities that are less than perfectly positively correlated are combined in a portfolio. In this case, the risk of the portfolio, as measured by its standard deviation, will be less than the weighted average of the securities’ standard deviations.

Question 22

James purchases one call option on BFA stock. The exercise price of this option is $25 a share. BFA stock is listed on the TSX. Which statement about this transaction is correct?
A. James has a short position in the option.
B. James has the right to buy 100 shares of BFA at $25 a share at any time on or before the options expiry date.
C. James must buy 100 shares of BFA at $25 a share at any time on or before the options expiry date.
D. James is the writer of the option.

Answer 22

B is correct.

James has the right to buy 100 shares of BFA at $25 a share at any time on or before the options expiry date.

Option holders have rights, not obligations. If it is not in the option holder’s financial interest to exercise the option, he does not have to do so.

Question 23

Sam purchases a put option on CDG stock. The strike price of this option is $18 a share. When will Sam most likely exercise his option on CDG stock?
A. He will exercise his option to sell if the market price of CDG stock falls below $18 per share and his option becomes in-the-money.
B. He will exercise his option to sell if the market price of CDG stock exceeds $18 per share and his option becomes out-of-the-money.
C. He will exercise his option to sell if the market price of CDG stock falls below $18 per share and his option becomes out-of-the-money.
D. He will exercise his option to buy if the market price of CDG stock exceeds $18 per share and his option becomes in-the-money.

Answer 23

A is correct.

Sam will likely exercise his option to sell CDG stock if the market price of CDG stock falls below $18 per share and his option becomes in-the-money. A put option gives the buyer the right to sell at a certain price. The option owner will exercise the option only if it is in his financial interest to do so, which means that the option must be in-the-money. A put option is considered in-the-money when the market price of the underlying asset is lower than the option’s strike price. If it is, the put owner can exercise the right to sell the underlying asset at the higher strike price and immediately buy it back at the lower market price.