Asset Beta vs Unlevered Beta: Market Risk Analysis & Calculation Method

Asset Beta vs Unlevered Beta: Market Risk Analysis & Calculation Method

What are asset beta and unlevered beta?

The asset beta of the firm will be contingent upon the financing structure, whether via debt or equity. In most instances, the business will be funded by both stock and debt. A business is classified as leveraged when it has borrowed capital and unleveraged when it lacks debt capital. It signifies that an unleveraged business is entirely funded via equity capital. The unleveraged beta of a business, sometimes referred to as the asset beta, represents the company's beta without the effects of debt. The asset beta quantifies the volatility of the company's returns independent of its financial leverage. The asset beta of the business will assess the risk of an unleveraged corporation relative to the market risk. It is referred to as the asset beta because the volatility of the firm, which is not influenced by debt financing, is solely attributable to its assets. The asset beta may be calculated using the below formula:

Equity beta is ascertained by the gradient of the returns of the ship portfolio and the excess market risk. The beta coefficient is calculated using the accompanying formula;

Beta equals zero. In Microsoft Excel, the beta value, representing the slope, is 1.268504.

The company is presumed to have a tax rate of zero, hence t = 0.

is characterized as the debt-to-equity ratio. This research use Damodaran's industry average debt-to-equity (D/E) ratio, which is 0.75.

The asset beta will be calculated as outlined above.

Asset beta = 1.268504 / 1 + 0.75 = 1.268504 / 1.75 = 0.725

Beta is a metric of market risk that analyzes the regression of a stock relative to the market index, often the S&P 500. In calculating a firm's beta, the debt-to-equity ratio is often assigned significant importance, since it reflects the company's leverage. Unlevered Beta assesses a firm's market risk without accounting for its leverage or the effects of its debt. An unlevered assessment excludes any benefits or drawbacks related to debt. The term "systematic risk" denotes hazards that a corporation cannot remove or minimize independently. Systemic hazards are very challenging to mitigate or evade due to their omnipresent characteristics. A kind of risk that might be difficult to manage is referred to as systemic risk. Examples of this category of risk including warfare, inflationary pressures, and natural calamities. Beta is a metric that quantifies the historical systematic risk or volatility experienced by a company or portfolio. The risk correlates with the stock's volatility; decreased volatility results in less risk. Conversely, more volatility correlates with less risk. A business with a beta of one indicates that its overall risk is commensurate with that of the market. Since beta was less than 1 in our example, this signifies that the company's volatility was inferior to that of the whole market. A business with a beta of 2 indicates a volatility level that exceeds that of the entire market.

The equation for calculating asset beta

The amount of debt a business has may affect its performance, hence increasing the firm's vulnerability to stock price swings. Despite the company's indebtedness, the unlevered beta model assesses it as if it were debt-free by excluding any debt-related factors from the computation. Analysts may use unlevered beta to compare businesses or the market, given the variations in capital structures and debt levels across various firms. Only if a corporation's assets (equity) are susceptible to market fluctuations will they be considered.

Multiple methodologies exist for appraising the choice. Among the methods used in stock option valuation is the Black-Scholes model. This is a crucial contemporary financial theory used for asset valuation. The model is deemed relevant since it incorporates the time value of money by factoring in the risk-free rate and duration. The model is regarded as one of the finest due to its acknowledgment of return volatility. Stock volatility is quantified by the standard deviation. The asset appraisal using the Black-Scholes model will include the standard deviation. 

When calculating the option price with the Black-Scholes option pricing model, the analyst must adhere to the following assumptions:

The company has not distributed dividends during the duration of the option. This indicates that the corporation is keeping all its profits, resulting in a 0% dividend payout ratio.

The market is presumed to be perfectly competitive, with no government interference. The pricing mechanism is determined by the law of demand and supply.

The options are presumed to be European options, exercisable just at expiry.

Another assumption required for determining the option's value using the Black-Scholes model is that asset returns follow a log-normal distribution.

The trading of options is presumed to incur no transaction costs. This indicates that the option purchaser will not bear the transaction expense.

In the option calculation, we will assume that the risk-free rate and the asset or security volatility are known and remain constant during the study period.

The below formula is used to ascertain the asset's worth;

C equals

P denotes the option price.

P represents the current price of the stock or the underlying asset.

E denotes the exercise price, whereas r signifies the risk-free interest rate.

T represents the period to maturity, whereas N is used in the calculation of the cumulative normal distribution.

The assessment of option value via the Black-Scholes option pricing model will include the following steps:

Step 1: Calculation of d1 and d2.

Significance of beta in assessing market risk

d 1 =

Step 2: Calculation of the cumulative normal distribution

0.5 + 0.4967 = 0.9967

0.5 - 0.4918 = 0.0082

Step 3: Utilize the calculated numbers above to determine the option's value using the option pricing methodology.

C equals  

8091.21 - 29.403 = 8061.81

We demonstrate that statistically comparable patterns may emerge within a dynamic capital structure model, which posits that firms regularly reassess the advantages of their investment and financing decisions. We are building upon the foundational approach established by Hennessy and Whited (2005, 2007) for dynamic corporate and investment-oriented asset price evaluations. Merton's compound option pricing formula (1973) and Toft and Prucyk's (1997) valuation of an equity option for a business subject to taxes and bankruptcy expenses are seminal contributions that directly influence the implementation of a dynamic firm model in option pricing. Both writers evaluate the pricing of a stock option for a firm that has taxation and bankruptcy expenses. Geske, Subrahmanyam, and Zhou (2016) assert that including the impact of leverage mitigates pricing inaccuracies compared to the conventional Black-Scholes model (1973). Leverage influences option pricing, and similar to the compound option model, skewness in the risk-neutral distribution may arise from a dynamic firm model (e.g., a downward-sloping implied volatility surface). Despite the company's endogenous investment program presenting a restricted array of development opportunities, a substantial interaction persists between the impact of leverage and the economic potency of the alternatives. The equilibrium implied volatility surface is contingent upon the prevailing conditions and may exhibit several forms, including an upward slope, a downward slope, a U-shape, or an inverted U-shape. The accumulation of growth alternatives results from the model's prospective investment opportunities and the existence of capital adjustment costs, which render the investment process discontinuous. Both elements enhance the model's overall adaptability. The model's main source of economic uncertainty, namely productivity shock, is defined as a persistent stochastic process, allowing for the anticipation of future investment opportunities. Prolonged productivity shocks result in a decline in an option's implied volatility over time.

The Black-Scholes model assumes that stock prices adhere to a lognormal distribution since asset values cannot be negative, as they are constrained by zero. Contemporary financial markets often exhibit right skewness and kurtosis in asset values, indicating fat tails. The market encounters downturns linked to elevated risk levels much more often than a normal distribution would suggest.

Assuming asset values adhere to a lognormal distribution, the Black-Scholes model forecasts uniform implied volatilities across all strike prices. Since the 1987 market collapse, the implied volatility of at-the-money or out-of-the-money options has been lower than that of in-the-money or out-of-the-money options. This occurrence is increasing due to the market factoring in a heightened likelihood of a significant downturn. The volatility skew we see arises from the manifestation of this phenomenon. By plotting the implied volatilities of options with identical expiry dates, one may generate a "grin" or "skew" pattern on a graph by amalgamating the two sets of implied volatilities. The Black-Scholes model is fundamentally inadequate for ascertaining the implied volatility of an option.

Valuation of options via the Black-Scholes model

The Black-Scholes model, in contrast, does not consider that American options may be exercised prior to their expiration date when computing option values in Europe. Nevertheless, the model incorporates assumptions about risk-free rates and payments that may not accurately reflect real-world scenarios. The model's premise is inconsistent with the reality that volatility fluctuates in reaction to changes in supply and demand levels.

Moreover, additional assumptions, including the lack of transaction costs or taxes, the uniformity of the risk-free interest rate across maturities, the allowance for short selling with the proceeds, and the nonexistence of risk-free arbitrage opportunities, may result in prices that diverge from those observed in reality. In reality, prices are seen to be as follows:

Excluding taxes, commissions, and many other trading expenses, it is probable that values will vary from actual outcomes. This is an additional situation in which divergence may arise.

Fundamental analysis may be used to assess the worth of the firm. The fundamental analysis approach use financial statement data to ascertain the firm's worth. The analyst must ascertain the firm's cash flow and, given that these would be projected cash flows, the analyst will need to calculate their present value via discounting. The firm's cash flows' present value will equal the present value of the yearly cash flow plus the present value of the terminal cash flow.

Fundamental analysis is a technique used to determine a stock's intrinsic value. It does this by integrating information from several sources, including market fluctuations and news headlines, with the accessible financial data. It is crucial to remember that the "intrinsic value" of a stock, sometimes referred to as its "fair value," does not fluctuate abruptly. This study may be used to identify the firm's critical components and evaluate its value by considering both macroeconomic and microeconomic characteristics (Wafi, Hassan & Mabrouk, 2015). Fundamental analysis suggests that a company's share price may not accurately represent its intrinsic worth. It is often either excessively priced or offered at a reduced rate.

Fundamental analysis allows for the prediction of long-term market trends. Long-term investors like it since it offers an indicator of the stock's anticipated worth. Furthermore, it assists in identifying potentially profitable investment opportunities, particularly those with a substantial rate of return.

A further benefit of the research is its assistance with a crucial but intangible variable: business acumen. This element, when examined within the context of an investment analysis, might provide significant insights into the future of a certain company.

The weighted average cost of capital (WACC) will be calculated using the Capital Asset Pricing Model (CAPM). The cost of capital is calculated as follows:

Weighted Average Cost of Capital (WACC) =

The cost of capital, to be used as the discount rate in the appraisal, will be calculated as shown below;

Cost of capital = 0.0555

Cost of capital (r) equals 5.55%

Terminal cash flow is defined as the cash flow the business will produce at the project's conclusion. In this study, it is crucial to ascertain the worth at the conclusion of 2032. The calculated value the company is anticipated to generate will be the terminal value. The terminal value is calculated using the following formula.

Terminal value equals

Let g represent the rate of increase in cash flow. The growth rate of sales is presumed to be denoted as g, whereas r represents the firm's cost of capital.

The firm's worth is equivalent to the present value of cash flows combined with the present value of the terminal value. This is calculated in the table below;

The first stage in assessing the investment in bonds or their management is to evaluate the chance of default for the business exposure over a specified investment duration. Numerous experts will derive their parameter estimations by comparing the outcomes from the published values of the rating agencies.

The default rate will be calculated using several approaches. One of the ways will address the calculation of the withdrawals. The approach will disregard withdrawals, and no adjustments will be made for them.

The possibilities of default risk are delineated variably by distinct rating agencies. The likelihood of default risk to be used for this study is the mean default risk probabilities of the specified firms. The average odds of default risk are 5%.

The above graphic demonstrates a significant likelihood, also known as default risk or default probability, that a debtor will not meet the obligations of the debt security to which they have committed. Another aspect of credit risk is the magnitude of the loss, whereas default risk is one of the two dimensions of credit risk (Antunes, Gonçalves & Prego, 2016). The valuation of credit default swaps and other derivatives, such as government and corporate bonds, must include default risk considerations (CDS). Evaluating the default risk of these instruments is more critical than quantifying the potential loss that may arise in the event of failure. This is due to the reduced default rates linked to high-quality bonds (Giglio, 2016).

The valuation of financial instruments and their corresponding returns are mostly affected by the default risk linked to these assets. Due to the association between elevated default risk and increased interest rates, bonds with higher default risk often have more challenges in accessing capital markets. This is due to the correlation between elevated interest rates and increased default risk, which may impact financing possibilities.

References

Ammar, S. B. (2020). Catastrophe risk and the implied volatility smile. Journal of Risk and Insurance, 87(2), 381-405.

Antunes, A., Gonçalves, H., & Prego, P. (2016). Firm default probabilities revisited. Economic Bulletin and Financial Stability Report Articles.

Geske, R., Subrahmanyam, A., & Zhou, Y. (2016). Capital structure effects on the prices of equity call options. Journal of Financial Economics, 121(2), 231-253.

Giglio, S. (2016). Credit default swap spreads and systemic financial risk (No. 15). ESRB Working Paper Series.

Wafi, A. S., Hassan, H., & Mabrouk, A. (2015). Fundamental analysis models in financial markets–review study. Procedia economics and finance, 30, 939-947.