# Portfolio Choice in a Multiasset World

#### Written by Leon Clarenbach

#### Grade 1.3

#### Paper category

### Term Paper

#### Subject

### Business Administration>Management

#### Year

### 2020

#### Abstract

Term Paper: Annual return and annualized standard deviation. At first glance, Tesla stock TSLA performs significantly better than other stocks, with an average annual return rate of close to 350%, and the second best-performing Zoom (ZM) stock, compared to Below only roughly an average of 183% in that time frame. Regarding the improvement in returns, Tesla's performance was significantly better than the other stocks in the portfolio. However, it is worth noting that TSLA started at the lowest price per share at the beginning of the observation time frame, which was only $45, and ZM was $92.46 per share. In contrast, Amazon’s starting price is already high at $1,789.84 per share, but it is still able to generate an annual return rate of more than 95%, and reached a stock price of $3,450.96 at the end of the measurement period. Regarding the standard deviation, TSLA shows the highest price volatility, which is not ideal from an investor's point of view, because it shows that the stock brings inconsistent returns to its stock owners and can therefore be regarded as a riskier investment . Zoom stock presents the second largest variance, so it is also the standard deviation in the portfolio. We can see that the return during the year is volatile. However, this is not the only indicator of stock quality, and given that high returns are not the main disadvantage for investors. Since the investment strategy of this portfolio focuses on high innovation, but compared with its fair value, the degree of market capitalization is higher, and high volatility can be expected. In contrast, Amazon is the most stable stock with an annual standard deviation of only 41%, followed by Netflix, rounded to 52%. In Chart 1, you can see the average performance of all four stocks plotted on the chart over the past year. The graph shows the performance of the average annual return (y-axis) in relation to the risk as the standard deviation (x-axis). Tesla's stock can be seen as the outlier in the upper right corner. You can also see in the graph that Table 1 shows the highest standard deviation and highest risk. Regarding the mean variance standard that shows that risk and return are related, Tesla dominates other stocks. The ratio in Table 2 is calculated by dividing the annual standard deviation by the annual average return to show how much risk the investor must bear in return. For Tesla, we can see that the average risk percentage in the past year is 28.11% of the average return, which is the lowest percentage in the portfolio. In this regard, Netflix can be regarded as the riskiest stock because almost 60% of the return is represented by risk. Amazon and Zoom are at similar levels in terms of mean variance standards, which means that they offer similar rates of return and similar risks expressed by standard deviations.
2.4. Minimum Variance Portfolio The author calculated the Minimum Variance Portfolio to measure the minimum risk that a particular combination of stocks in the investment portfolio can bear. It aims to minimize volatility, thereby reducing the market risk of the portfolio to the lowest point related to returns, so investors will not take more risk than necessary. The total minimum possible variance of the portfolio in this paper, from the co-variance table and individual variance, is 0,0003995, and the standard deviation is 0,0199885. Compared to the variance of a standard portfolio of equal weights, this means that volatility is reduced by nearly 40%. At the same time, it must observe that the return on the portfolio has shrunk by nearly 50% (0.0049 to 0.0026346 MV return). This means that investors have the lowest volatility or risk in this portfolio. Expected return. Table 4 shows the minimum variance of the four stocks in the minimum variance portfolio. It can be observed that the minimum variance of TSLA is negative as the only position. This is because this is the riskiest stock, so the share of the stock in the minimum variance portfolio must be minimized. In the same argument, Amazon has the largest weight in the smallest variance portfolio, close to 80%, because this stock has the smallest variance and therefore the least risk: in order to achieve the smallest possible variance, the share of the least volatile stock should be correspondingly , The stock ZM with the second lowest volatility has the second highest weight, about 0.15, and the NFLX has the second lowest volatility, and the second lowest weight, with a weight of about 0.10. Here, the restriction on short selling is actually different, because the TSLA weight described in Table 4 is negative, as shown in Table 5. This means that the best option in the smallest variance portfolio is to short the stock because of the risk, which means betting on a price drop instead of buying the actual stock, that is, betting on a price increase. 2.5. Tangent portfolio risk-free interest rate with appropriate agency is the theoretical return rate of investment without any risk (Chen, 2020a). For the purposes of this article, the risk-free interest rate is calculated without considering the current inflation rate. As an appropriate agent, the author chose the daily yield curve (2020) of US government bonds published by the US Department of the Treasury, starting from the first date calculated from the stock price of the portfolio, that is, September 3, 2019. Obtain a higher long-term stable return with a 30-year rate of return. This figure reached 1.95%. Read Less