Question

A. What is the correlation coef. between these two?

Consider these historical annual returns for the MDY, mid-cap ETF and DHI, a mid-cap homebuilding company. Date Return MDY DHI 12/31/106.120% -2.040% 12/31/11 26.300% 23.040% 12/31/12 9.810% 16.848% 12/31/13 14.830% 7.864% 12/31/14 -2.430% 3.944% 12/31/15 -2.670% -7.136% 12/31/16 -38.250% -32.600% 12/31/17 12.500% 13.000% 12/31/18 32.650% 26.120% 6.540% 5.449% 20.490% 18.007% Avg Stdev

B.  Assume that MDY represents the market of mid-cap stocks and you are a mid-cap-stock-only investor. Which is the DHI's beta?

C. Historically, has DHI been more or less volatile than the mid-cap stock market, as approximated by MDY?

D. For the purpose of this question (irrespective of your prior answers) assume DHI is less volatile than the mid-cap market. What best explains this?

--------a) The absolute value of DHI's beta is less than 1, and its standard deviation is less than MDY's.

------b) DHI works in a staid, steady-state industry, and should therefore should be expected to be less volatile than the entire mid-cap market.

--------c) The absolute value of DHI's beta is greater than 1, and its standard deviation is less than MDY's.

Answer 1

A). Correlation coefficient = where

(Rm – R1) * (Rd – R2))/ ((Rm – R1)2* (Rd – R2)?)

Rm = return of MDY; R1 = average return of MDY; Rd = return of DHI; R2 = average return of DHI

Correlation coefficient = 1.5479

Calculations:

(Rd-R) -7.49% (Rd-R)^2 0.00560835 2 Date 12/31/10 12/31/11 12/31/12 12/31/13 12/31/14 12/31/15 12/31/16 12/31/17 12/31/18 Total (T) Return ('R) Standard deviation (SD) MDY (Rm) 6.12% 26.30% 9.81% 14.83% -2.43% -2.67% -38.25% 12.50% 32.65% 58.86% 6.540% DHI (RD) -2.04% 23.04% 16.85% 7.86% 3.94% -7.14% -32.60% 13.00% 26.12% 49.04% 5.449% (Rm-R) -0.42% 19.76% 3.27% 8.29% -8.97% -9.21% -44.79% 5.96% 26.11% 0.00% (Rm-R)^2 0.00001764 0.03904576 0.00106929 0.00687241 0.00804609 0.008482411 0.20061441 0.00355216 0.06817321 33.59% 11.40% .42% -1.50% -12.58% -38.05% 7.55% 20.67% 0.00% 0.01299397 0.00058328 0.00022647 0.01583794 0.14477179 0.00570193 0.04272948 25.94% (Rm-R)*(Rd-R) 0.031% 3.476% 0.373% 0.200% 0.135% 1.159% 17.042% 0.450% 5.397% 28.26% (Rm-R)^2* (Rd-R)^2 0.000% 0.121% 0.001% 0.000% 0.000% 0.013% 2.904% 0.002% 0.291% 3.33% 20.490% 18.007%

B). For beta calculation of DHI, MDY can be taken as the market return.

Beta(Rd, Rm) = Covariance(Rd, Rm)/Variance(Rm) = Correlation*StDev(DHI)*StDev(MDY)/Variance(Rm)

= 1.5479*20.490%*18.007%/(20.490%^2) = 1.3603

C). DHI has lower standard deviation than MDY so historically, it has been less volatile than MDY.

D). Statement C is correct. Absolute value of DHI's beta is more than 1 and it has lower standard deviation than MDY. This indicates that it is less volatile than the market.