How leverage can improve performance

. One of the best-known Capital Asset Pricing Model (CAP/M) provides us with a methodology for measuring the relationship between the risk premium and the impact of leverage on expected returns. However, this model is not used only to value the cost of capital but also to evaluate the performance of managed portfolios. We will test how the expected return changes in percent by changing the debt-equity ratio and the tax rate based on following assumptions: market return 7%, risk-free rate of return 1% and beta 1.2. These assumptions will be constant and we will change the debt-equity ratio and tax rate. Based on these results, it is clear that the change in profitability varies, in relation to the change of the DE ratio by one tenth. As for changes I n tax rates, changes in expected profitability are not entirely in direct proportion to these changes.


Introduction
Leverage causes two problems: it increases the company´s risk to shareholders and can also cause the company to go bankrupt in bad times. The total risk of the company can thus be divided into business risk (without debt) and financial risk (with debt).

Methods
We started with characteristics of the model. Subsequently, we used this model with variants by changing variables. These solutions are presented in tabular form. As companies in real life respond to the change in interest rates, we observed the four largest companies in the United States by market capitalization. We also compared the DE ratio with the ROE ratio to prove whether the theory holds.

Beta and leverage
One of the best-known model Capital Asset Pricing Model (CAPM) provide us with a methodology for measuring the relationship between the risk premium and the impact of leverage on expected returns. The model was created by Sharpe [1] and Lintner [2] to estimate the cost of capital for project selection.
A survey by Graham and Harvey [3] that up to 73.5% of CFOs use this model in decision making. However, this model is not used only to value the cost of capital but also to evaluate the performance of managed portfolios. In the literature we can find many studies that point to different returns using different strategies [4,5,6] and results for equally and value-weighted portfolios [7,8,9]. Other studies have shown [10,11,12] that the CAPM applies in January, a month when inflation is usually low, important macroeconomic indicators are announced, and also in months when investors can borrow cheaply. This model is presented as one of the most important model in the financial economy [4,5]. Even Berk and van Binbergen [13] found in their work that this model is closest to the models used by the investor in capital allocation decisions.
Some authors also included macroeconomic factors [14], or human capital [15], or growth in consumption [8].This model has the following basic formula: The risk premium is calculated: If the company has no debt, then in this case the has unlevered beta β U , so the company has only business risk, By adding debt to the balance sheet, the company has also financial risk and the beta is called levered beta β L .
Then the relationship between the unlevered and levered beta is as follows: Or: By modifying the original formula by unlevered and levered be, then we get the equation:

Results
We will test how the expected return changes in percentage by changing the debt-equity ratio and the tax rate based on the following assumptions: market return 7%, risk-free rate of return 1%, beta 1.2. These assumptions will be constant and we will change the debt-equity ratio and tax rate.  Change in return in % 0 -1,26 % -5,74 % As for the changes in tax rates, the changes in expected profitability are not entirely in direct proportions to these changes, as it was the case in the previous case.

Discussions
The largest company is characterized as a publicly traded company with the largest market capitalization. Data are as of 31.3.2020. To this date was Microsoft largest company (MSFT) with a market capitalization of 1.2 billion of US dollars. Its historical development of DE ratio for the previous 5 years was:  In 2018, the Fed´s key interest rate reached its maximum (within the period under review). If we monitor the interdependence of the DE ratio and ROE, then in 2017 was the value of the ROE indicator the second highest (after 2019).
The second most valuable company is Apple (AAPL) with a market capitalization of 1.11 billion US dollars. Compared to MSFT, the ratio is still increasing. This company thus not relate to changes in interest rates. On other hand, the increase in debt also leads to an increase in the ROE ratio, which was the highest in the last year.
The third largest company is Amazon (AMZN) with a market capitalization 0,97 billion US dollars. The development of the DE ratio is very similar to MSFT.
The development of the ratio is in the following table. The DE ratio was also the highest in 2017 and also rose in 2019 when the Fed began to reduce interest rates. However, it is in conflict with previous companies because in 2017 was the ROE indicator the second lowest (after 2015). The increase in indebtedness thus did not support the growth of the ROE ratio.
The latest company is Alphabet (GOOG or GOOGL) with a market capitalization of 0.8 Billion US dollars. Compared to the other previously mentioned companies, it has the lowest values of the DE ratio. This indicator has also not changed significantly.  This company thus not take an advantage of debt financing. This is also confirmed by the ROE values, which are significantly lower than the previously mentioned companies.

Conclusions
Some companies seek to take advantage of low interest rates to increase shareholder value, other such as AAPL ignore this possibility. Other large companies are adjusting their DE ratio according to the current situation on the credit market. Another exception concerns Amazon, which has kept the DE ratio low for a long time. This was ultimately reflected in the value of the ROE ratio, which was the lowest of all examined companies.