cyber21

Three portfolios with normally distributed returns are available to an investor who wants to minimize the probability that the portfolio return will be less than 5%. The risk and return characteristics of these portfolios are shown in the following table:

Portfolio	Expected return	Standard deviation
Epps	6%	4%
Flake	7%	9%
Grant	10%	15%

Based on Roy’s safety-first criterion, which portfolio should the investor select?

A) Epps.

B) Grant.

C) Flake.

---

Roy’s safety-first ratios for the three portfolios:
Epps = (6 - 5) / 4 = 0.25
Flake = ( 7 - 5) / 9 = 0.222
Grant = (10 - 5) / 15 = 0.33
The portfolio with the largest safety-first ratio has the lowest probability of a return less than 5%. The investor should select the Grant portfolio.

cyber21

The mean and standard deviation of four portfolios are listed below in percentage terms. Using Roy's safety first criteria and a threshold of 3%, select the respective mean and standard deviation that corresponds to the optimal portfolio.

A) 5; 3.

B) 14; 20.

C) 19; 28.

---

According to the safety-first criterion, the optimal portfolio is the one that has has the largest value for the SFRatio (mean − threshold) / Standard Deviation. A mean = 5 and Standard Deviation = 3 yields the largest SFRatio from the choices given: (5 − 3) / 3 = 0.67.

cyber21

The safety-first criterion rules focuses on:

A) SEC regulations.

B) margin requirements.

C) shortfall risk.

---

The safety-first criterion focuses on shortfall risk which is the probability that a portfolio’s value or return will not fall below a given threshold level. The safety-first criterion usually dictate choosing a portfolio with the lowest probability of falling below the threshold level or return.

cyber21

If the threshold return is higher than the risk-free rate, what will be the relationship between Roy’s safety-first ratio (SF) and Sharpe’s ratio?

A) The SF ratio will be lower.

B) The SF ratio may be higher or lower depending on the standard deviation.

C) The SF ratio will be higher.

---

Since each ratio has the standard deviation of returns in the denominator, the difference depends upon the effect on the numerator. Since both the risk-free rate (in the Sharpe ratio) and the threshold rate (in the SF ratio) are subtracted from the expected return, a larger threshold rate would result in a smaller SF ratio value.

cyber21

The mean and standard deviation of three portfolios are listed below in percentage terms. Using Roy's safety-first criteria and a threshold of 4%, select the respective mean and standard deviation that corresponds to the optimal portfolio.

A) 14; 20.

B) 19; 28.

C) 5; 3.

---

According to the safety-first criterion, the optimal portfolio is the one that has the largest value for the SFRatio (mean − threshold) / Standard Deviation. A mean = 19 and Standard Deviation = 28 yields the largest SFRatio from the choices given: (19 − 4) / 28 = 0.5357.

cyber21

The farthest point on the left side of the lognormal distribution:

A) is skewed to the left.

B) can be any negative number.

C) is bounded by 0.

---

The lognormal distribution is skewed to the right with a long right hand tail and is bounded on the left hand side of the curve by zero.

cyber21

Which of the following statements regarding the distribution of returns used for asset pricing models is most accurate?

A) Normal distribution returns are used for asset pricing models because they will only allow the asset price to fall to zero.

B) Lognormal distribution returns are used for asset pricing models because they will not result in an asset return of less than -100%.

C) Lognormal distribution returns are used because this will allow for negative returns on the assets.

---

Lognormal distribution returns are used for asset pricing models because this will not result in asset returns of less than 100% because the lowest the asset price can decrease to is zero which is the lowest value on the lognormal distribution. The normal distribution allows for asset prices less than zero which could result in a return of less than -100% which is impossible.

cyber21

If a random variable x is lognormally distributed then ln x is:

A) abnormally distributed.

B) normally distributed.

C) defined as ex.

---

For any random variable that is normally distributed its natural logarithm (ln) will be lognormally distributed. The opposite is also true: for any random variable that is lognormally distributed its natural logarithm (ln) will be normally distributed.

cyber21

If random variable Y follows a lognormal distribution then the natural log of Y must be:

A) denoted as ex.

B) normally distributed.

C) lognormally distributed.

---

For any random variable that is lognormally distributed its natural logarithm (ln) will be normally distributed.

cyber21

Given Y is lognormally distributed, then ln Y is:

A) a lognormal distribution.

B) the antilog of Y.

C) normally distributed.

---

If Y is lognormally distributed, then ln Y is normally distributed.