# Level 1 CFA® Exam:

Return & Risk in Equity Market

When an investor purchases shares, his or her total return is affected by two factors: price change and dividend income. A price change is the difference between the purchase price and the sale price, while dividend income comes from the income generated by the company and paid to its shareholders. So, the total return may be calculated using this formula:

\(R_{t} = \frac{(P_{t} - P_{t-1}) + D_{t}}{P_{t-1}}=\frac{P_t+D_t}{P_{t-1}}-1\)

- \(R_{t}\) - equity security's total return
- \(P_{t-1}\) - purchase price
- \(P_{t}\) - sale price
- \(D_{t}\) - cash or stock dividends paid at the end of the holding period

Of course, this formula is useful for companies that actually make dividend payments – these are usually companies in the mature stage. As you probably know, in the case of companies in their early stages usually all income of companies is reinvested and dividend is not paid. And so, the total return equals the price appreciation divided by the purchase price. Let's look at an example.

Suppose that the price of an RDG, Inc. share at the end of 2020 was USD 12.34, while at the end of 2021 it increased to USD 13.56. All the company’s profit is paid in the form of dividends. If the dividend per share paid in 2021 was USD 1.98, what was the total return on this company's shares?

We apply the formula for the total return.

\(R_{t}=\frac{P_t+D_t}{P_{t-1}}-1=\frac{13.56+1.98}{12.34}-1=25.93\%\)

Please remember that if you invest in foreign equity, the total return also depends on foreign exchange gains or losses. Here's an example.

A German investor bought shares of a Swiss Green Company for 25 Swiss francs each. After three months, he sells them for 25.50 Swiss francs each. What is the investor’s total return if we take foreign exchange gains into account and assume that during the investment period the Swiss franc appreciated against the euro by 3%?

(...)

Remember:

- If the foreign currency in which we hold the investment and which we get after selling shares appreciates against our domestic currency, we should add appreciation to total return to compute the approximate value of total return including foreign exchange gains.
- If the foreign currency in which we hold the investment and which we get after selling shares depreciates against our domestic currency, we should subtract depreciation from the total return to compute the approximate value of total return including foreign exchange losses.

The risk of any equity security is connected with cash flows an investor receives from an instrument he holds. To be more precise, it results from the uncertainty of future cash flows. When uncertainty rises, risk increases as well and that leads to higher volatility of the security price. To measure the risk of a given security, we generally use the standard deviation of the expected return or variance.

There are a few ways in which we can estimate the expected future return and risk. For example, we can use average historical return and standard deviation of return in the estimation of future standard deviation.

You can also estimate possible future returns and their probabilities and based on this data compute the expected return and standard deviation.

Note: Level of risk depends on the type of shares. As you've probably guessed common shares are riskier than preference shares. It is so because dividends on preference shares are specified and they are paid before dividends on common shares. Additionally, if a company is liquidated, preference shareholders are usually satisfied before common shareholders.

Also: Putable shares may be sold at a pre-determined price, so the level of risk associated with them is lower than in the case of callable shares which can be repurchased by the issuer. What is more, callable shares are riskier than shares without embedded options.

There are 2 main reasons why a company issues shares:

- to raise its capital,
- to increase its liquidity.

The capital is raised to finance planned expenditures, such as the purchase of equipment, research and development, or takeovers. In some cases, raising capital can be required by supervisory institutions which order companies to uphold a certain level of their financial ratios to ensure the stability of financial markets. The capital adequacy ratio used by banks may serve us as an example here.

2 concepts are strongly related to issuing shares and these are:

- the book value, and
- the market value.

(...)

In the case of the book value of equity, we very often compute the book value of equity per share. It can be obtained this way:

\(BVPS=\frac{\text{total shareholders' equity}}{\text{no. of shares outstanding}}\)

- \(BVPS\) - book value of equity per share

The ratio used to compare the market value and the book value is the price-to-book ratio. Take a look at the formula:

\(\text{price-to-book ratio}=\frac{\text{market price per share}}{\text{book value of equity per share}}\)

If the ratio is greater than 1, it means that the company's market price is higher than its book value. If the ratio is lower than 1, it means that the company's market price is lower than its book value.

What's important here is that usually, you should not compare price-to-book ratios of companies operating in different industries. This is because of the different characteristics of various businesses.

To measure how efficiently the management of a company uses the company’s capital, you can use return on equity (ROE). ROE gives you information on how much net income was generated thanks to the capital provided by the shareholders.

This measure is given by the following formula to be used in your level 1 CFA exam:

\(ROE_{t} = \frac{NI_{t}}{\text{Average }BVE_{t}} = \frac{NI_{t}}{\frac{BVE_{t-1} + BVE_{t}}{2}}\)

- \(ROE_{t}\) - return on equity for year "t"
- \(BVE_{t}\) - total book value of equity at the end of year "t"
- \(BVE_{t-1}\) - total book value of equity at the end of year "t-1" (= beginning of year "t")
- \(NI_{t}\) - net income for year "t"

**Note:** If we assume that only equity at the begining of the year was used to generate net income for the year, the formula for the return on equity looks as follows:

**\(ROE_{t} = \frac{NI_{t}}{BVE_{t-1}}\)**

Because in this formula we use the average total book value, it means we assume that net income was generated not only by the equity existing at the beginning of the year but also by the equity acquired during these 12 months. Let's have an example.

An investor is considering the purchase of shares of White Bridge Company. To learn whether the equity provided by investors is used efficiently, he wants to compute ROE for this company. He knows that net income in 2021 was USD 21,000. From the company's balance sheet he learned that the book value at the end of 2020 was USD 430,000, while a year later it was USD 470,000.

What is the value of return on equity?

(...)

There is also another way to compute ROE. In the second approach, we assume that net income was generated only by the equity existing at the beginning of the year. Have a look at the formula:

\(ROE_{t}=\frac{NI_{t}}{BVE_{t-1}}\)

The first formula should be used in the case of the high volatility of the book value while the second one requires the book value to be stable.

In this case, an important issue is how net income and the book value are computed. The results often depend on the choice of accounting methods and, thus, comparing ROEs of different companies may be difficult.

Is an increasing ROE always good?

There are at least two situations when the answer is 'no'. ROE can increase when net income falls more slowly than the shareholder's equity. This situation isn't beneficial to the company. Another situation could be when a company issues debt to repurchase its own shares. Then ROE increases, but the company’s debt increases also.

The income of an investor is an investor’s minimum required rate of return.

When a company wants to obtain capital, it must incur some costs. It is in the company's best interest to minimize those costs. The two sources of capital are debt and equity.

(...)

- Total return on investment includes capital gains, that is the difference between the sale price and the purchase price, as well as the dividend income.
- If the foreign currency in which we hold the investment and which we get after selling shares appreciates against our domestic currency, we should add appreciation to total return to compute the approximate value of total return including foreign exchange gains.
- The risk of a financial instrument stems from uncertainty concerning its future cash flows.
- Common shares are riskier than preference shares.
- There are 2 main reasons why a company issues shares: 1) to raise its capital and 2) to increase its liquidity.
- The book value is the difference between the company's assets and liabilities.
- The market value depends on a kind of sentiment of investors and their expectations for the company’s future cash flows.
- The book value reflects past decisions of the company’s management, whereas the market value reflects the decisions of investors made on the grounds of expected cash flows.
- ROE is computed as the product of net income and the book value of equity while the book value of equity is the difference between the company's assets and its liabilities.
- The company’s cost of debt is equal to the investors' minimum required rate of return.
- The company’s cost of equity may differ from the investors' minimum required rate of return.