Stock Valuation and Risk: How to Value Stocks and Measure Risk

Book: Financial Markets and Institutions, 11th Edition Author: Jeff Madura Publisher: Cengage Learning, 2015 Series: Chapter 11 Review

How much is a stock actually worth? That is the central question of Chapter 11. And the honest answer is: it depends on who you ask and what model they use. Madura walks through the main valuation methods, explains how risk gets measured, and then tackles whether markets are even efficient enough for any of this to matter.

Three Ways to Value a Stock

The Price-Earnings (PE) Method

This is the simplest approach. Take a company’s expected earnings per share and multiply it by the average PE ratio of its industry. If a firm expects $3 per share in earnings and the industry PE ratio is 15, the stock is valued at $45 per share.

Simple, right? But there are problems. Different investors forecast different earnings. They disagree on which companies should be included in the “industry” for comparison. And PE ratios change over time. So even if two investors agree on earnings, they might still get different valuations.

The Dividend Discount Model

This one goes back to 1931, when John B. Williams figured out that a stock’s price should equal the present value of all future dividends. If a stock pays $7 per share forever and investors require a 14% return, the stock is worth $50 ($7 / 0.14).

If dividends grow at a constant rate, you use the constant-growth version: Price = D1 / (k - g), where D1 is next year’s dividend, k is the required return, and g is the growth rate. A stock paying $7 next year with 4% growth and a 14% required return is worth $70.

The catch? This model struggles with companies that do not pay dividends. And many growing companies reinvest everything. For those firms, you need the adjusted version, which combines expected dividends with a forecasted sale price based on future earnings and industry PE ratios.

The Free Cash Flow Model

For firms that skip dividends entirely, you estimate future free cash flows, subtract liabilities, and divide by the number of shares. It sounds straightforward, but getting accurate free cash flow estimates is notoriously difficult. Accounting rules allow enough flexibility that the numbers can be misleading.

How to Determine the Required Rate of Return

This is where the Capital Asset Pricing Model (CAPM) comes in. The idea is that the required return on a stock equals the risk-free rate plus a risk premium based on the stock’s sensitivity to overall market movements.

The formula: Rj = Rf + Bj(Rm - Rf)

Beta (Bj) measures how much a stock moves relative to the market. A beta of 1.2 means that for every 1% the market moves, the stock is expected to move 1.2%. Higher beta means more risk, which means investors demand a higher return.

For a stock with a beta of 1.2, a risk-free rate of 6%, and a market risk premium of 7%, the required return is 14.4%. That number then feeds into whatever valuation model you are using.

What Moves Stock Prices

Madura breaks it into three categories.

Economic factors include GDP growth, interest rates, and exchange rates. When the economy grows, corporate cash flows tend to grow too, pushing stock prices up. Higher interest rates raise the required return and push prices down. A weak dollar helps exporters but hurts importers.

Market factors include investor sentiment and seasonal patterns. The “January effect” describes how small stocks tend to outperform in January because portfolio managers shift toward riskier stocks at the start of the year. There is also a “weekend effect” and a “holiday effect,” though these patterns tend to fade once enough investors try to exploit them.

Firm-specific factors include dividend changes, earnings surprises, and acquisitions. An earnings beat pushes a stock up. A dividend cut signals trouble. Acquisition targets usually see their stock price jump.

Measuring Stock Risk

Risk comes down to uncertainty about future returns. Madura covers three ways to measure it.

Volatility is the standard deviation of returns. Higher volatility means more uncertainty. For portfolios, volatility depends not just on individual stock volatility but also on how stocks are correlated with each other. Low correlation between holdings reduces overall portfolio risk.

Beta measures sensitivity to market movements. A portfolio of high-beta stocks will get crushed when the market drops but will also outperform during rallies. The VIX index, derived from S&P 500 options, is essentially a real-time measure of expected market volatility. It spiked during the 2008 crisis and fell as conditions stabilized.

Value at Risk (VaR) estimates the maximum expected loss over a given period at a given confidence level. If a stock has a 95% VaR of -3.2% per day, you can expect the daily loss to be no worse than 3.2% on 95% of trading days. For a $20 million position with a VaR of -3%, the maximum daily dollar loss is $600,000.

The limitation? VaR depends on historical data. If you measure it during calm times, you will underestimate the risk of a crisis. The 2008 meltdown made this painfully clear.

Performance Measurement

Two indexes help evaluate risk-adjusted returns.

The Sharpe Index divides excess return (return minus risk-free rate) by standard deviation. It rewards high returns and low volatility.

The Treynor Index divides excess return by beta. It measures return per unit of systematic risk.

A stock can look great on one index and mediocre on the other. Which one you prefer depends on whether you think total risk or systematic risk is more relevant.

Market Efficiency

If markets are efficient, stock prices already reflect all available information, and no one can consistently earn abnormal returns.

Weak-form efficiency says past price data is already priced in, so technical analysis does not work. Evidence mostly supports this, though anomalies like the January effect exist.

Semistrong-form efficiency says all public information is reflected in prices, so fundamental analysis does not help either. Studies show prices adjust quickly to announcements, but IPOs tend to be underpriced on the first day.

Strong-form efficiency says even insider information is already reflected. This is the hardest to support. Insider trading clearly generates abnormal returns, which is why it is illegal rather than impossible.

My Take

The Enron case study in the appendix is the real star of this chapter. It shows how every safeguard failed: auditors signed off on fake numbers, analysts were afraid to downgrade, board members sold their own stock, and rating agencies missed $7 billion in hidden debt. The valuation models are only as good as the data going into them.

I also think the CAPM is taught more often than it is trusted. Beta changes over time, the market risk premium is hard to estimate, and the whole model assumes investors only care about systematic risk. Real investors care about all kinds of risk. Still, CAPM gives you a framework, and that is better than guessing.

The VaR discussion is particularly relevant after 2008. Using calm historical periods to estimate future risk is like checking the weather on a sunny day and concluding you will never need an umbrella.

Previous: Stock Offerings and Investor Monitoring Next: Market Microstructure and Trading Strategies