# School of Stocks Calculating Covariance Matrix and Portfolio Variance in Excel

For example, if an asset manager can reap a 10% return on a specific Mutual Fund against a benchmark index of 8%, his/her alpha ratio would be 2. Investors opt to invest as per the alpha ratio in Mutual Funds around 1.5. Note that the alpha ratio in Mutual Funds should be considered based on a mean of previous performance and not just on current data. R-Squared measures the extent to which the performance of a dependent variable is due to the independent variables. However, it doesn’t tell the impact of each independent variable on the correlation of variables.

• If you are using the latest version of Microsoft Office 365, you can directly hit enter after inputting all the required arrays in the MMULT function to generate the output.
• A beta of 1.0 indicates that the stock has same risk as that of market i.e., if the market rises by 1%, then price of the stock also increases by 1%.
• Dilution rate of 2% is on the higher side given the growth projections.
• Calculating beta requires the danger-free fee, inventory’s rate of return, and market rate of return.
• A. Although it depends on the industry and situation of the company, basic key lies in the discounting the future earnings to the present value.

The calculation of Sharpe and Sortino ratio is almost the same with one major difference – Sortino ratio only shows downside volatility i.e. volatility in down markets. The second limitation of Sharpe ratio, as well as the Sortino ratio, is that it does not distinguish between market risk and excess risk over market. Beta is calculated by using regression analysis and applying the concept of the line of best fit. It is calculated with respect to a market benchmark index, say, Nifty, or BSE Sensex.

However, beta measures how large the change in the fund returns with respect to its benchmark. The primary difference between the two is that the adjusted R-Squared considers the effect of each of the independent variables against the dependent variable, and R-Squared doesn’t. If the new variable’s effect is more, the value of the adjusted R-Squared will increase, and vice versa. However, the R-Squared value will increase if the model adds new independent variables. Mutual fund investors use this to determine the extent to which the benchmark index is responsible for the change in the fund’s returns. A beta of 1.0 indicates that the stock has same risk as that of market i.e., if the market rises by 1%, then price of the stock also increases by 1%.

A 60% value indicates the benchmark is responsible only for 60% of changes in the fund’s net asset value or NAV. A 100% value would mean the benchmark is fully responsible for the change in the fund’s return. The value varies between zero to one and, as a percentage, ranges from zero to 100%.

So, how does one identify a stock’s systematic and unsystematic risk? If a stock has a total risk of 15%, how much of it is due to the market factors and how much is due to the internal factors? In statistics, standard deviation and beta are two well-known tools that are used for risk analysis.

## The beta factor of securities

If the value is close to one or 100%, then the dependent variable’s performance is highly affected by the independent variable. In contrast, if the value is low , then the behaviour of the dependent variable is not explained by the independent variable. In L1 if you invest Rs 500 at the beginning of the year you will earn Rs 50 as profit by the end of the year. Similarly, if you invest Rs 500 in L2 at the beginning of the year you will earn Rs 100 as profit by the end of the year.

It can increase and change by adding more independent variables. This is where adjusted R-Squared comes into the picture. Adjusted R-Squared tells how reliable the correlation of dependent and independent variables is and the impact of the correlation due to adding a variable.

To calculate the beta coefficient of a single inventory, you will need to gather the day by day closing costs over a given time period. You will also collect the day by day closing prices for a benchmark market index over the identical time interval. The broad equity market has a beta coefficient of 1 and beta coefficients of various shares are measured close to the market beta. What the capital asset pricing mannequin supplies is a consistent means to price risk premiums.

It just indicates the sensitivity of a stock to the market’s movement. But you don’t have to get into the fundamentals of such calculations as beta calculation in excel MS Excel provides simple functions to calculate such statistics. Unsystematic risks are also known as internal risks and are diversifiable.

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We will learn CAPM beta, flaws in regression beta, Calculation of Raw and Adjusted Beta, Effect of operating leverage and financial leverage in build-up beta, calculation of Industry beta. The beta Mutual Funds formula is Covariance/Variance of Market’s Returns. Suppose, an ELSS Fund’s CAPM was shown as 5%; later, its actual returns turned out to be 8%. This difference is indicative of the fact that the asset manager was able to produce 3% more profits than was anticipated.

A figure of 0 in the case of alpha is indicative of an asset manager’s performance graph to be precisely in line with the benchmark index. Any number in the negatives would suggest the asset manager’s performance https://1investing.in/ as underwhelming. Further, alpha in mutual funds beyond 0 showcases the fund manager’s achievement of outperforming the benchmark index. It is also known as the coefficient of determination.

Additional capital is assumed to be raised at current price to book value ratio. If the current book value is high, adjust the number accordingly. Using too high dilution rate will result in significantly higher valuation. In spreadsheet ERP, which calculates equity risk premium, enter monthly values of BSE 200 index. Model assumes that a business growing at a high growth rate has higher risks than a business that is slowing down or has reached a mature phase. Model uses Return on Equity as the measure of profitability.

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We have already calculated the covariance matrix in the previous section. In this chapter, we will explain how to calculate correlation matrix and covariance matrix comprising of multiple stocks, in Microsoft Excel. We will also explain how to calculate portfolio variance and standard deviation, in Excel. In financial markets, the inter-relationships between economic variables have a direct or indirect influence on the performance of asset classes like equities, debt and gold. For example, in a 12 months where the broad market or benchmark index returns 25% above the chance free price, suppose two managers achieve 50% above the danger free price. Whether traders can count on the second manager to duplicate that performance in future periods is in fact a unique question.

## How to use MS-Excel to understand the relation between financial variables

If you are keen to accept greater dangers to get greater returns, then it is sensible to demand a higher return for a better threat; otherwise, why take the higher danger. By comparing the beta of a stock and its historic return with that of the overall market, you can determine whether the return of a stock is value its risk. A beta that’s greater than 1.0 indicates that the security’s price is theoretically more volatile than the market. For example, if a inventory’s beta is 1.2, it’s assumed to be 20% more risky than the market. Technology stocks and small caps tend to have greater betas than the market benchmark. This indicates that adding the stock to a portfolio will increase the portfolio’s risk, but also increase its expected return.

Your expectations for future in terms of future ROE the business is likely to generate, future growth rates of earnings that business can achieve, and riskiness of the business. Y range must be the stock prices range for the particular company or the industry and X range should cover the complete market index values. So far we have discussed what is alpha and beta in mutual fund, let us see how alpha and beta in mutual fund are calculated.

It is an indicator of a inventory’s systematic threat which is the undiversifiable risk inherent in the whole monetary system. It’s a simple way to rapidly assess your entire portfolio’s volatility. If you highlight cells A7 or E7, you’ll see the formula to fetch the data. We will learn to prepare equity research and valuation report from scratch by using skills we learned, researching about the company, quarterly con calls, analysing annual reports, etc. We will learn financial models using international FAST standards.

Now that we have both the individual stock weights and the covariance matrix, the final step is to calculate the portfolio variance. In the image below, see how we have calculated the portfolio variance and annualized standard deviation. In layman terms, risk is the deviation from expected or average returns.