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# Relationship Between Long-run Rate of Stock Market Appreciation and Sustainable Growth Rate

Potential economic growth is vital to investors. Potential GDP is used to measure the productive capacity of an economy. Investors are concerned if the earnings growth is related to or limited by the GDP growth rate.

The growth earnings exceed the GDP growth only if the ratio of corporate earnings to GDP rises over time. However, in the long run, the long-run earnings growth cannot exceed the GDP growth since the portion of the profits of the GDP cannot increase forever.

## Relationship Between Stock Prices and Economic Growth

To evaluate this relationship, we write the aggregate value of the stock market as the product of two critical ratios. Denote $$P$$ as the total price of the equities and $$E$$ as the aggregate earnings. Then:

$$P=GDP\left(\frac{E}{GDP}\right)\left(\frac{P}{E}\right)$$

Considering this equation, it is easy to see that the aggregate value of the equities can be represented as the product of GDP, the ratio of corporate earning to GDP, and the market’s price-to-earnings ratio. It is important to note that corresponding variables should be used if the GDP quote is real or nominal.

The equation above can be rewritten into logarithmic changes over the investment horizon $$T$$. That is:

$$\left(\frac{1}{T}\right)\%\Delta\ P=\left(\frac{1}{T}\right)\%\Delta GDP+\left(\frac{1}{T}\right)\%\Delta\left(\frac{E}{GDP}\right)+\left(\frac{1}{T}\right)\%\Delta\left(\frac{P}{E}\right)$$

The equation above implies that the stock market value is equivalent to the addition of change in GDP, a percentage in the share of earnings, and a percentage in price-earnings multiple.

If we consider short to immediate investment horizons, all three factors lead to appreciation or depreciation of the stock price. However, the GDP growth becomes a significant factor in the long run since the second and third terms of the equation above tend to be zero. Therefore, it is worth noting that factors affecting the GDP are ultimately the same as those of the market price performance.

## Question

Which of the following factors would most likely positively impact the per capita GDP of a developed country with high capital per worker?

1. Saving and investment.
2. Technological improvement.
3. Existence of free trade.

#### Solution

The correct answer is B.

The country is developed and has high capital per worker. Therefore, technological advancement would see increased productivity and hence, per capita GDP.

A is incorrect. The country already has high capital to labor ratio, and therefore increased saving or investment is unlikely to increase the growth of its per capita GDP unless it employs technology.

C is incorrect. Most developed countries have substantially low trade barriers. Thanks to this, free trade will not have an incremental impact on the per capita GDP.

Reading 7: Economic Growth

LOS 7 (b) Describe the relation between the long-run rate of stock market appreciation and the sustainable growth rate of the economy.

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