Understanding Financial Risk and Asset Valuation

Posted on May 17, 2024 in Economy

Duration Gap Analysis

Market value-based model used to measure and manage interest rate risk. It involves calculating the difference between the average duration of a bank’s assets and the duration of its liabilities.

Macaulay Duration

Measures the average financial life of an asset or liability and is calculated as the weighted average of the maturities of the cash payments. The formula for Macaulay duration: where: m= maturity

Modified Duration

Expresses the interest sensitivity of an asset or liability’s value and is calculated as Macaulay duration divided by 1 plus the market interest rate. The formula for modified duration is: ytm: bond’s yield

PV

One dollar today is worth more than a dollar tomorrow due to the ability to invest and earn interest immediately. Present value represents the value today of a cash flow received in t years’ time and is calculated by multiplying the cash flow by a discount factor

NPV

Financial concept used to evaluate the profitability of an investment by calculating the present value of expected cash flows generated by the investment and comparing it to the initial cost of the investment. If NPV is positive, the investment is financially viable.

IRR

Rate at which the present value of cash inflows equals the present value of cash outflows, makes NPV=0. Limitations: assumes reinvestment of cash flows at the same rate as the IRR itself, which may not always be realistic. Also may not provide a clear indication of the actual value or scale of an investment, especially when comparing projects with different cash flow patterns or when there are multiple changes in the cash flow direction. Multiple IRRs occur when cash flows of the investment project change direction more than once, making it challenging to interpret the result accurately.

Payback Period

Financial metric used to evaluate the time it takes for an investment to recover its initial cost through generated cash flows. Provides quick assessment of an investment’s liquidity and risk. Limitations: doesn’t consider time value of money, discounting future cash flows, or the profitability of an investment beyond the payback period. Also ignores cash flows after the payback period.

Bonds

Fixed-income securities issued by governments to raise capital. Represent a loan by an investor to the issuer. Different types: Coupon bonds pay periodic interest payments to bondholders based on a fixed coupon rate applied to the bond’s face value. The interest payments are typically made semi-annually or annually until the bond matures, when the issuer repays the principal amount to the holder. Zero coupon bonds don’t make periodic interest payments, they are issued at a discount to their face value and redeemed at face value upon maturity. The return to the investor is the difference between the purchase price and the face value of the bond

Dividend Discounted Model

Value common stocks based on the PV of expected future dividends. Zero growth model assumes a constant dividend stream where dividends remain the same over time. P= DIV/ r Gordon growth model: valuing a stock that assumes dividends will grow at a constant rate indefinitely. P= D/(r-g)

Weighted average of expected returns Standard deviation show how variable returns are around average return. Expected return on a portfolio: Portfolio variance:

Benefits of Diversification

1. Risk reduction: Diversification helps spread investment risk across different assets, by holding a diversified portfolio investors can reduce the impact of negative events. 2. Enhanced returns: Diversification can improve overall portfolio returns by capturing gains from different asset classes that perform well at different times. 3. Increased flexibility: Diversification provides flexibility to adjust portfolios based on changing market conditions.

Mean-Standard Deviation Portfolio

Identify optimal allocation of risky assets for a risk-averse investor by minimizing risk. Assumes that investors base their preferences solely on expected portfolio returns and return standard deviations. Involves calculating risk and return for individual securities and portfolios.

Efficient Frontier

Represents a group of portfolios that minimizes risk for a given level of expected return and maximizes expected return for a given level of risk when there is no risk-free asset. Illustrates the trade-off between risk and return for different portfolio combinations of risky assets. The optimal portfolio without a risk-free asset is the portfolio that lies on the efficient frontier and provides the highest expected return for a given level of risk or the lowest risk for a given level of expected return.

Capital Market Line

Represents a linear relationship between the risk and return of portfolios that combine the risk-free asset with a risky portfolio of assets. Starts at the risk-free rate and extends to the point where the tangent line from the risk-free rate touches the efficient frontier of risky assets. This tangent point represents the optimal portfolio, known as the market portfolio, which combines the risk-free asset with the market portfolio of risky assets. Provides a clear depiction of the optimal risk-return combinations available to investors when a risk-free asset is included in the investment universe.

Asset Pricing Models

Frameworks used to determine the fair price of financial assets in equilibrium. These models help investors understand the relationship between risk and return and guide investment decisions. Two asset pricing models are Capital Asset Pricing Model and Arbitrage Pricing Theory.

CAPM

Key asset pricing model that determines the equilibrium price of risky assets based on the trade-off between risk and return. Assumptions: 1. Investors are rational and risk-averse. 2. Investors have homogeneous expectations. 3. There are no taxes or transaction costs. 4. All investors have access to the same information. 5. Investors can borrow and lend at the risk-free rate. 6. All assets are infinitely divisible. 7. The market is in equilibrium. Equation: where beta= σiM / σm^2. Beta represents the sensitivity of an asset’s returns to the market returns. A beta of 1 indicates that the asset moves in line with the market, while a beta greater than 1 signifies higher volatility compared to the market.

CAPM has theoretical limitations due to unrealistic assumptions like infinite borrowing at the risk-free rate and no personal taxes, impacting its applicability in real-world scenarios. Practical limitations of the CAPM include challenges in testing the model due to the unobservability of the market portfolio, making it difficult to empirically validate the model.

Market Premium

Additional return that investors expect to receive for holding a risky asset over the risk-free rate. It represents compensation for bearing the systematic risk associated with investing in the overall market. Calculated as the difference between the expected return on the market portfolio and the risk-free rate

Security Market Line

Graphical representation of CAPM equilibrium relationship between risk and return. Shows the expected return of an asset as a function of its beta, which measures its sensitivity to market movements. Starts at the risk-free rate and slopes upward, reflecting the risk premium investors demand for taking on systematic risk. Assets on or above the SML are considered fairly priced. X axis: beta.

Arbitrage Pricing Theory

Asset pricing model that suggests that the expected return of a financial asset can be determined by its exposure to various systematic risk factors. Alternative of CAPM and based on the absence of arbitrage opportunities in the market. Assumptions: 1. Investors are rational and risk-averse. 2. No arbitrage opportunities exist in the market. 3. Securities are priced based on their exposure to multiple risk factors. 4. Investors have access to the same information and can trade costlessly.

Expected Risk Premiums in APT

Expected return of an asset is a linear function of its sensitivity to various risk factors. The risk premiums are determined by the factor sensitivities of the asset. The APT does not specify the exact number or nature of the risk factors but suggests that assets with similar factor sensitivities should have similar expected returns.

Theoretical and Empirical Validation of APT

Model’s theoretical strength lies in its ability to accommodate multiple risk factors and provide a more flexible framework for pricing assets compared to CAPM. However, APT’s empirical validation can be challenging due to the need to identify and measure relevant risk factors accurately. APT’s reliance on identifying the appropriate risk factors and the difficulty in estimating their risk premiums accurately contribute to the challenges in its empirical validation.

Factor Models

Used to explain the variations in asset returns based on common factors that influence multiple assets simultaneously. The basic idea is that all common variations in stock returns are generated by movements in one or more factors. A simple one-factor model assumes that variations in asset returns are driven by a single factor, while more complex multi-factor models consider multiple factors affecting returns. The model helps in understanding the systematic risk factors that impact asset returns and provides a framework for analyzing and pricing assets based on their sensitivities to these factors. Play a crucial role in APT. Simplest factor model.

Informationally Efficient Markets

Market where asset prices fully reflect all available information, making it impossible for investors to consistently achieve excess returns based on that information. The theoretical framework for informational efficiency is based on the Efficient Market Hypothesis, which posits that asset prices reflect all available information, making it difficult for investors to outperform the market consistently. Three forms of market efficiency: 1. Weak-form efficiency: Prices reflect all historical information, including past prices and returns, making it impossible to profit from analyzing historical data. 2. Semi-strong-form efficiency: Prices incorporate all publicly available information, such as financial statements and company announcements, quickly and accurately. Investors cannot consistently earn excess returns based on public information. 3. Strong-form efficiency: Prices reflect all public and private information, including insider information. In a strongly efficient market, even insider information cannot be used to achieve excess returns.

The EMH has significant implications for security analysis and trading strategies. It suggests that technical analysis, fundamental analysis, and insider trading may not consistently lead to outperformance in an efficient market. It has been a subject of extensive empirical research, with evidence supporting varying degrees of market efficiency across different markets and time periods.

Concept of Excess Returns

Difference between the actual return on an asset and the expected equilibrium return. In an efficient market, excess returns are minimal as asset prices reflect all available information, making it challenging for investors to consistently earn abnormal profits based on that information. Excess return at time t

Joint hypothesis problem arises in testing the efficient market hypothesis when calculating excess returns. It refers to the challenge of accurately quantifying abnormal returns due to the limitation in validating pricing models like CAPM and APT.

Empirical evidence on efficient markets has been a subject of extensive research, with studies providing insights both in favor of and against market efficiency.

Evidence in Favor of Market Efficiency

1. Early empirical tests support market efficiency, particularly in weak-form and semi-strong-form efficiency. 2. Studies have shown that stock prices exhibit random walk behavior, indicating weak-form efficiency. 3. Rapid incorporation of new and unexpected information into stock prices supports semi-strong-form efficiency. 4. Empirical evidence on mutual fund performance aligns with strong-form efficiency, leading many funds to adopt passive management strategies.
Evidence Against Market Efficiency: 1. Anomalies such as the small firm effect challenge the random walk behavior of stock prices, suggesting deviations from weak-form efficiency. 2. Market overreaction and underreaction to new information indicate inconsistencies with semi-strong-form efficiency. 3. Excess returns of corporate insiders and anomalies like calendar effects and mean reversion behavior of stocks go against the efficient market hypothesis