Calculation of Mean, Standard Deviation and Efficient Portfolio

Investment management

Contents
EXECUTIVE SUMMARY.......................................................................................................................3
MAIN BODY.............................................................................................................................................4
1. Calculation of the Arithmetic Mean (AM), Geometric Mean (GM) and Standard Deviation (σ) of
returns of each of the five asset classes....................................................................................................4
2. Construction of an efficient portfolio.............................................................................................11
3. Discussion on Modern Portfolio Theory (MPT) models................................................................13
CONCLUSION........................................................................................................................................16
REFERENCES........................................................................................................................................17

EXECUTIVE SUMMARY
The report abstracts about different aspects regarding to analysis of given assets. In first
and second question, information about calculation of different kinds of mean, standard deviation
is included in order to assess risk-return features. In the end part of report information related to
various types of modern portfolio theories is mentioned along with impact of diversification is
also summarized.

MAIN BODY
1. Calculation of the Arithmetic Mean (AM), Geometric Mean (GM) and Standard
Deviation (σ) of returns of each of the five asset classes.
Arithmetic mean (μ)- In the context of statistics, term arithmetic mean can be defined as
an average of given data set (Qian, Yang and Chu, 2019). In relation to given information
about return of various five assets calculation of arithmetic mean is done below in such
manner:
Arithmetic mean (μ)= Sum of data/ number of data
Australian
Shares
Australian
Bonds
US Shares US Fed
Funds
Brent Oil
Sum of data 104.90 77.5 153.55 33.04 199.60
Number of data 20 20 20 20 20
Calculation 104.90/20 77.5/20 153.55/20 33.04/20 199.60/20
Arithmetic mean 5.25 3.85 7.68 1.65 9.98
Geometric Mean - This can be understood as a form of mean which typically shows
central tendency of given data set by help of making product of values (Lu, Ma and
Zhang, 2020). In relation to given data set of five assets, calculation of geometric mean is
done below in such manner:
Formula of geometric mean: n√x1.x2.x3......x n
Spread sheet formula: =PRODUCT (A1:A6) ^ (1/COUNT (A1:A6))
Spread sheet formula: =PRODUCT (A1:A6) ^ (1/COUNT (A1:A6))
Australian
Shares
Australian
Bonds
US Shares US Fed
Funds
Brent Oil
Geometric Mean 9.42 3.32 0.69 14.63