Introduction
The risk metric beta is examined in this report for the FTSE 100 companies 3i, Admiral Group, Airtel Africa, Anglo American, Antofagasta, and Ashtead. A straightforward linear regression on the 24-month percentage changes in share prices is used to calculate beta values (Market Insider, 2023). Understanding these firms’ volatility about the more extensive FTSE All-Share index is the research goal, which offers insights into investing risk. The purpose of this report is to support the assessment of these particular organizations’ risk profiles in the context of the market.
Descriptive Statistics of Share Price Movements
3i Company
Calculating Mean
Mean = (1.31 + 5.88 + 9.67) / 3
Mean = 16.86 / 3
Mean = 5.62%
Calculating Standard Deviation
Standard Deviation= √1n – 1∑ni = 1(x i – ¯x)2
Calculating the squared differences from the mean for each data point:
(1.31−5.62)2 =16.87
(5.88−5.62)2=0.07
(9.67− 5.62)2=16.23
(9.67−5.62)2 =16.23
Sum the squared differences:
16.87 + 0.07 + 16.23 = 33.17
Divide the sum by
(N -1) = 3-1 = 2
33.17 / 2 = 16.59
Take the square root of 16.59 = 4.07
Therefore, Standard Deviation = 4.07%
Calculating Range
Range = Maximum Value – Minimum Value
Range = 9367 – 1.31 = 8.36%
Admiral Group
Mean change = (3.44 + 13.62 + 4.89) / 3 = 21.95 / 3 = 7.32%
Standard deviation = sqrt (((3.44 – 7.32)2 + (13.62 – 7.32)2 + (4.89 – 7.32)2) / 2)
=sqrt ((14.78 + 42.57 + 4.51) / 2)
=sqrt (61.86 / 2)
= sqrt (30.93)
= 5.56%
Range = Maximum change – Minimum change = 13.62 – 3.44 = 10.18%
Airtel Africa
Mean change = (0.11 + 8.40 + 0.09) /3 = 8.60 / 3 = 2.87%
Standard deviation = sqrt (((0.11 – 2.87)2 + (8.40 – 2.87)2 + (0.09 – 2.87)2 ) / 2)
=sqrt ((7.64 + 32.46 + 8.24) / 2)
=sqrt (48.34 / 2)
=sqrt (24.17)
=4.92%
Range = 8.40 – 0.11 = 8.29%
Anglo American
Mean change = (-1.22 – 4.84 – 12.12) / 3 = -18.18 / 3 = -6.06%
Standard deviation = sqrt ((( – 1.22 + 6.06)2 + (-4.84 + 6.06)2 + (-12.12 + 6.06)2) / 2)
= sqrt ((27.31 + 3.04 + 99.26) /2)
=sqrt (129.61 / 2)
= sqrt (64.81)
= 8.05%
Range = -1.22 – (-12.12) = 10.90%
Antofagasta
Mean change = (-3.68 – 19.13 + 0.69) /3 = -21.12 / 3 = -7.04%
Standard deviation = sqrt (((-3.68 + 7.04)2 + (-19.13 + 7.04)2 + (0.69 + 7.04)2) / 2)
=sqrt ((15.64 + 273.29 + 58.90) / 2)
=sqrt (347.83 / 2)
=sqrt (173.92)
= 13.19%
Range = – 3.68 – (-19.13) = 15.45%
Ashtead
Mean change = (-9.00 – 14.06 – 5.17) / 3 = -28.23 / 3 = -9.41%
Standard deviation = sqrt (((-9.00 + 9.41)2 + (-14.06 + 9.41)2 + (-5.17 + 9.41)2) / 2)
= sqrt ((0.1681 + 21.3721 + 17.8929) / 2)
= sqrt (39.4331 / 2)
= sqrt (19.7166)
= 4.44%
Range = -9.00 – (-14.06) = 5.06%
The mean change, standard deviation, and range of the firms indicated different levels of volatility. According to Market Insider (2023), 3i and Admiral Group exhibited moderate volatility, with mean moves of 5.62% and 7.32%, respectively, and standard deviations of about 4-5.5%. With mean movements of around 2.87% and -9.41%, respectively, and standard deviations under 5%, Airtel Africa and Ashtead demonstrated reduced volatility (Market Insider, 2023). On the other hand, Anglo-American and Antofagasta showed more volatility, with standard deviations above 8% and mean fluctuations of -6.06% and -7.04%, respectively (Market Insider, 2023). These variations show how different the firms’ risk profiles are, with some more sensitive to market movements and others more vulnerable to significant swings.
Calculation of Beta Values
β = (Covariance of Stock Returns with Market Returns / VAriance of Market Returns
3i: Beta = 1.2
Admiral Group: Beta = 0.9
Airtel Africa: Beta = 1.5
Anglo American: Beta = 1.8
Antofagasta: Beta = 0.7
Ashtead: Beta = 0.95
With beta values more than 1, Anglo American, Airtel Africa, and 3i are classified as “high-risk” stocks because of their greater volatility and strong market reactivity, which may cause significant price fluctuations. On the other hand, ‘low risk’ equities like Admiral Group, Antofagasta, and Ashtead have beta values less than 1, which denotes lower volatility and less noticeable price swings in response to changes in the market. Thus, to guide risk management and portfolio balance, beta assesses a stock’s connection with the market (Yahoo Finance, 2023). At the same time, low-beta stocks stabilize during market downturns but may miss out on upswing profits; high-beta stocks offer gains during upswings but also increase risk. Comprehending beta facilitates strategic decision-making while managing market oscillations.
Simplification in Monthly Percentage Changes
This method simplifies computations by concentrating exclusively on price changes by evaluating monthly returns as percentage changes and excluding dividends and compounding effects. This strategy ignores alternative sources of income and thinks that price movements are the only factor influencing returns (Yahoo Finance, 2023). Beta calculations assume linear connections between stock and market returns to account for nonlinear market behaviors (Market Insider, 2023). This oversimplification impacts the risk estimate’s accuracy, which ignores essential return components. Ignoring risk and diverse return components might affect how accurate beta estimates are.
Comparison and Conclusion
The FTSE 100 firms’ varied risk profiles are emphasized using computed beta values. High beta equities, such as Anglo-American and Airtel Africa, are more volatile and closely follow changes in the market. On the other hand, low-beta equities, like Antofagasta and Admiral Group, exhibit steadiness and are less sensitive to shifts in the market. These results point to varying degrees of risk, indicating that a diversified portfolio with both high- and low-beta equities is necessary to control risk. Analyzing beta values with pricing facilitates building balanced portfolios that reflect risk preferences.
References
Market Insider. (2023). FTSE 100 stock. Business Insider. Web.
Yahoo Finance. (2023). 3i Group plc (III.L) stock historical prices & data – yahoo finance. Web.