Question

The annual rates of return for Canadian common stocks and Japanese common stocks are provided in the following table:

Year	Canadian Common Stocks	Japanese Common Stocks
2014	-.141	.051
2015	.088	.229
2016	.280	-.224
2017	.050	.313
2018	.210	.155
2019	.220	.009

1. Compute the arithmetic mean rate of return and sample standard deviation of rates of returns for the two series. Discuss these two alternative investments in terms of their arithmetic average rates of return and their risk

2. Compute the geometric mean rate of return for each of these investments (markets).

Compare the arithmetic mean return and geometric mean return for each investment and discuss this difference between the two means as related to the standard deviation of each series.

Assess the quality of the approximation through comparison with the direct estimate of the sample variance.

3. Calculate the inflation-adjusted rates of returns for Canadian and Japanese stocks. What are the implications for a long-term investor? Assume the inflation rate is 3% in Canada and 4.5% in Japan.

Answer 1

Arithmentic mean computation

Year	Canadian common stocks	Japanese Common stocks
2014	-0.141	0.051
2015	0.088	0.229
2016	0.28	-0.224
2017	0.05	0.313
2018	0.21	0.155
2019	0.22	0.009
Total return for 6 years	0.707	0.533

Arithmetic mean = Total return for all periods / no. of periods

Arithmetic mean = Total return for 6 years / 6

Arithmetic mean for Canadian common stocks = 0.707/6 = 0.1178

Arithmetic mean for Japanese common stocks = 0.533/6 = 0.0888

Standard Deviation computation

Year	Canadian common stocks	Mean	Deviation from mean	Square of deviation from mean
2014	-0.141	0.1178	0.2588	0.0670
2015	0.088	0.1178	0.0298	0.0009
2016	0.28	0.1178	-0.1622	0.0263
2017	0.05	0.1178	0.0678	0.0046
2018	0.21	0.1178	-0.0922	0.0085
2019	0.22	0.1178	-0.1022	0.0104

Step 1: Sum of squared deviation from mean ---> 0.1177

Step 2 : Step1 / no. of preriods ----> 0.1177 / 6 = 0.0196

Step 3 : Square root of Step2 ---> 0.1401

Standard Deviation of Candian common stocks ---> 0.1401

Year	Japanese common stocks	Mean	Deviation from mean	Sqaure of deviation from mean
2014	0.051	0.0888	0.0378	0.0014
2015	0.229	0.0888	-0.1402	0.0197
2016	-0.224	0.0888	0.3128	0.0978
2017	0.313	0.0888	-0.2242	0.0503
2018	0.155	0.0888	-0.0662	0.0044
2019	0.009	0.0888	0.0798	0.0064

Step 1: Sum of squared deviation from mean ---> 0.1799

Step 2 : Step1 / no. of preriods ----> 0.1799 / 6 = 0.0300

Step 3 : Square root of Step2 ---> 0.1732

Standard Deviation of Candian common stocks ---> 0.1732

Summary of arithmetic returns and standard deviations

	Arithmetic returns	Standard Deviations
Canadian common stocks	0.1178	0.1401
Japanese common stocks	0.0888	0.1732

Based on summary it is evident that Canadian common stocks carry higher arithmetic returns and lower standard deviation in comparison to Japanese common stocks