Question

What is the geometric mean return of the stock?

What is the mean and the standard deviation of this stock?

What is the Total Holding Period Return?

Years	Stock Price	Stock Return
0	67
1	93	39%
2	110	18%
3	90	-18%
4	72	-20%
5	80	11%
6	66	-18%
7	95	44%

Answer 1

Computation of Holding period of return for each year:

Holding Period = (Income +(End of stock price - Opening stock price)) / Opening Stock Price

	A	B	C	D	E	F
Year	Stock Price	Stock Return	Income (A*B)	Appreciation (A - preceding A)	Opening Price (preceding A)	Holding Period [(C+D)/E]
0	67.00
1	93.00	39%	36.27	26.00	67.00	0.93
2	110.00	18%	19.80	17.00	93.00	0.40
3	90.00	-18%	-16.20	-20.00	110.00	-0.33
4	72.00	-20%	-14.40	-18.00	90.00	-0.36
5	80.00	11%	8.80	8.00	72.00	0.23
6	66.00	-18%	-11.88	-14.00	80.00	-0.32
7	95.00	44%	41.80	29.00	66.00	1.07

Computation of Geometric Mean of the stock:

Geometric mean = n√(1+r1)*(1+r2)………(1+rn)

Where,

                n = Number of years

                r = Rate of return every year

Geometric mean for the given stock is;

                = (7√(1+0.39)* (1+0.18)* (1-0.18)* (1-0.20)* (1+0.11)* (1-0.18)* (1+0.44)) - 1

                =( 7√1.39 * 1.18 * 0.82 * 0.80 * 1.11 * 0.82 * 1.44) - 1

                = (7√1.4103) - 1

                = 1.05 – 1

                = 0.05 or 5.00%

Computation of Mean and Standard deviation:

Mean		= [Σ(X)/n]
Standard Deviation	= √[Σ(X - X‾)^2/n]
Where X is the Return of asset every year
X‾ is the Mean

Year	Return (x)	X-X‾	(X-X‾)^2
1	0.39	0.31	0.0961
2	0.18	0.10	0.0100
3	-0.18	-0.26	0.0676
4	-0.20	-0.28	0.0784
5	0.11	0.03	0.0009
6	-0.18	-0.26	0.0676
7	0.44	0.36	0.1296
TOTAL	0.56		0.4502
Mean X‾	= 0.56/ 7	= 0.08 or 8%
Standard Deviation	= 0.4502 / 7 = 0.0643 or 6.43%