Download Portfolio management assignment and more Assignments Investment Management and Portfolio Theory in PDF only on Docsity!
NAME ADM NUMBER
KIMUTAI RUTH CHEPTOO 098597
WESLEY MBOYA WAMBUA 100437
MUTHEE JOY WANJIRU 100198
OTIENO WENDY LORNA AWUOR 097734
PORTFOLIO TERM PAPER
EXECUTIVE SUMMARY
How should private investors diversify? We were provided with a client who won a lottery and has limited financial knowledge. He wishes to invest in different asset classes but does not know which or how much to invest in each. We chose the following assets for him; Samsung Electronics, UK Gilt Futures, Euro Swiss France, Gold Futures, Toyota Japan, Safaricom, Bitcoin, and a 10 yr. Kenyan government bond.
We used five optimization methods including those under constrained and unconstrained mean variance from Markowitz (1952) Mean Variance Optimization. The file detailing how we optimized to arrive at the different portfolios and asset weights is provided and was done using Excel to calculate and represent the information. We compared the return statistics of each optimization method in order to achieve an analysis of the optimization. The average returns, standard deviations and Sharpe ratios among other values extracted from the optimization are discussed in the analysis. In the analysis of the data collected we discussed the normality of returns and its implication on our conclusion. The data on returns from 2016-2018 was graphically represented and compared to show the effect of the market fluctuations on the different portfolios. We used all this data to advise the client appropriately on which portfolio would fit their goals and would be the best for them in terms of utility. INTRODUCTION According to Markowitz, diversification is key for mean-variance portfolio optimization. Diversification is the use of mathematical models to find securities to place in a portfolio such that the portfolio has the highest possible return for its level of risk. Markowitz used this strategy that seeks to combine in a portfolio’s assets with returns that are less than perfectly correlated, in an effort to lower portfolio risk without sacrificing return. Therefore, how should our client or any investor allocate capital among the possible investment choices? Markowitz (1952)
less sensitive to changes in currency markets or global effects. But at the same time these small companies can still benefit from the financial liquidity and support of their central banks. We shall now explain why we chose some assets and how they are a better investment decision. Bitcoin, a cryptocurrency was chosen because of a lower risk of inflation and a lower falling risk compared to other currencies. This is because Bitcoin is a global currency that does not depend on government policy that can fail and cause hyperinflation or complete collapse of the currency. Another advantage is that it cannot be traced since once the seller gets the money it cannot go back to the buyer by any means thus no government can trace the source of your funds. The potential gains in bitcoin are more than the potential loses. This is because several crypto- analysts have speculated that Bitcoin could become a global currency in the future. Bitcoins is considered as commodity money, so when you hold Bitcoins you can invest them the same way you can invest in a business with flat money. Like flat currency, you’ll generate interest on this investment as well, so holding some Bitcoin can allow you to invest them and earn interest on the same. Moreover, you can receive good returns at increased prices on your investments too as time elapses. We also chose Safaricom because it is a denominator of the NSE. The brand has been raking in crazy profits for the past 8 years, something that has a direct bearing on the performance of the share at the NSE. In 7 years, the profit change for the brand has been 41.7 billion shillings. 2018 FY Results have shown why the share is the best bet for a long-term investment with an estimated return on investment being 37 percent annually. Service revenue for 2018 was 224. billion shillings. Profit before tax was 79.9 billion shillings. Profit after tax was 55.3bn. Imagine paying 24.6B in taxes. You can already ask yourself how much was going to the shareholders through the dividend channel then. Safaricom PLC continues to be a major contributor to government revenues remitting 43. billion shillings in duties taxes and license fees for the period ended in 30th September 2017. It has remitted 536 .5 billion shillings in taxes since inception. Now, ask yourself, how much have shareholders gotten since inception? This is the best option to invest in for the period 2018/ and the numbers talk for themselves. Safaricom is a critical listed brand and it’s a sure good and positive investment opportunity for one to get into if they had the capital.
Five optimization processes were used. They are The Short Sale-Unconstrained Maximum Sharpe Ratio, The Short Sale-Unconstrained Minimum-Variance, The Short Sale-Constrained Maximum Sharpe Ratio, The Short Sale-Constrained Minimum-Variance and the 1-norm Constrained Minimum Variance (with a standard deviation of 160%). There are two essential characteristics of a portfolio according to Markowitz (1952); its expected return and a measure of the dispersion of possible returns around the expected return, the variance being the most tractable estimate (Farrell 1976). In the mean variance optimal portfolio, the investor optimizes the trade-off between the mean and the variance of portfolio returns.
ANALYSIS
Descriptive statistics SAM-SK SCOM GCZ9 TOY-J KEN10Y R
BTC FLGZ9 EUR/CHF
- Kurtosis
Optimization A short sale is the sale of an asset, we, the sellers don’t own. This being a transaction in which one is advised to sell the assets if one is anticipating a decrease in the price of the asset. Doing so, we are required to return the same amount of number of shares in the days to come. In the optimizations done, the constraints were;
- Weights should be equal to 100%
- In the constrained optimizations, short selling was not allowed.
- In the 1-Norm optimization the absolute weights of the assets should have a sum of less than or equal to 160% Sharpe ratio analysis 2015 2016 2017 2018 Unconstrained minimum variance
Unconstrained maximum sharpe ratio
Constrained maximum sharpe ratio
Constrained minimum variance
1-norm constrained minimum variance
From the above data we see that the unconstrained minimum variance would be desired since it has the highest average of sharpe ratio over the four years followed by the unconstrained maximum sharpe ratio. The constrained methods have the lowest average in all years. 36-month return
We used the returns from 2016-2018 since they are the most recent years for our analysis. After we were able to 36 month returns and plotted a graph showing the performance of each optimization method on our portfolio, the curves were able to indicate the operation of these methods; in terms of consistency, volatility and even effectiveness in yielding high returns for our client. The unconstrained minimum variance method and unconstrained sharpe ratio have the highest returns and volatility but the slight differences show that minimum variance is better. Equally weighted portfolio
In our case study, we determine how best to advice a lottery winner concerning the best assets to invest in given the investor has little knowledge of where and how to invest. To this point, we have compared five Markowitz based optimization methods from our international diversification. Our main results can be summarized as follows, under the return averages the unconstrained minimum variance would be desired since it has the highest average all through making it more desirable. Under Sharpe ratio, the short-sale unconstrained minimum variance method of optimization yields a portfolio with the highest overall Sharpe ratio indicating that there is a higher return at every level of risk thus an investor would prefer investing in it. The data presented during analysis can also help us conclude that all of our portfolios are of normal distribution. Through analysis, we can finally advise the investor to invest in the portfolio optimized through the short sale-unconstrained minimum variance method. The equally weighted portfolio has a higher average return and skewness and also the short-sale unconstrained minimum variance portfolio has a lower standard deviation and kurtosis and has a higher Sharpe ratio overall. All this helps us conclude that the short-sale unconstrained minimum variance portfolio, is better at meeting the return-risk goals of the investor. REFERENCES
Jarrow, R. A (2018). Portfolio Optimization. In Continuous- Time Asset Pricing Theory (pp. 409-423). Springer, Cham. Pichler, A. (2018). Portfolio Optimization. Heinze, T. (2018). Portfolio Optimization using diversified efficient frontier. U.S Patent Application No. 15/431,199.
