# What is your forecast for the equity risk Premium? Assignment: Grinold Kroner Model (SEE provide PDF format question) First, some review: E(Re)=[D0(1+g)/(V0)] + g =[D1/(P0)] +g In the above equation, we make a simple modification to the infinite period dividend discount model, [Po=D1/k-g], to solve for the expected return on the market (thus we can forecast the price next year). In words, the price now equals the dividend next year divided by the required return less growth.

## QUESTION

Assignment: Grinold Kroner Model (SEE provide PDF format question)

First, some review:

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What is your forecast for the equity risk Premium? Assignment: Grinold Kroner Model (SEE provide PDF format question) First, some review: E(Re)=[D0(1+g)/(V0)] + g =[D1/(P0)] +g In the above equation, we make a simple modification to the infinite period dividend discount model, [Po=D1/k-g], to solve for the expected return on the market (thus we can forecast the price next year). In words, the price now equals the dividend next year divided by the required return less growth.
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E(Re)=[D0(1+g)/(V0)] + g =[D1/(P0)] +g

In the above equation, we make a simple modification to the infinite period dividend discount model,

[Po=D1/k-g], to solve for the expected return on the market (thus we can forecast the price next year).

In words, the price now equals the dividend next year divided by the required return less growth. The

above equations just solves for k. k is the same as E(Re) in the above equation. Sometimes we call it

expected return, or sometimes we call it required return. Same thing. If we have the price of a stock, or

an index value, and an estimate for next year dividend and growth we can estimate the expected

(required return) on the market. One way to estimate growth is using [retention rate x ROE].

Next, we can look at the infinite period dividend discount model.. Po=D1/k-g…and divided both sides by

earnings to provide some theoretical basis for the PE ratio. The PE ratio is a measure of relative value

and shows the value, or multiple, the investors are willing to pay to own a share of the earnings:

Pi/E1 = (D1/E1)/(k-g)

Shiller discusses the PE ratio measured with 10 year inflation adjusted numbers.

Our next step is to come up with another way to forecast for the market, using some of these ideas. The

associated reading with this assignment discusses the Grinold Kroner Model:

### Introduction

The estimation of the equity risk premium (ERP) is a crucial aspect of financial analysis and forecasting. It provides investors with insights into the expected returns on equities compared to risk-free investments. The Grinold Kroner Model offers a valuable framework for forecasting the equity risk premium by combining dividend discount models and fundamental factors. In this essay, we will explore the Grinold Kroner Model and provide a forecast for the equity risk premium based on its principles.

### Understanding the Grinold Kroner Model

The Grinold Kroner Model builds upon the concepts of expected return and dividend discount models. It acknowledges that the equity risk premium is influenced by both the dividend yield and the expected dividend growth rate (Grinold and Kroner Model – Breaking Down Finance, 2019). The model’s core equation, E(Re) = [D1/P0] + g, helps estimate the expected return on the market.

### Dividend Discount Model

The Grinold Kroner Model starts by considering the infinite period dividend discount model, Po = D1/(k – g). This equation establishes a theoretical basis for the price-to-earnings (P/E) ratio. By dividing both sides of the equation by earnings, we arrive at the expression Pi/E1 = (D1/E1)/(k – g), where Pi/E1 represents the P/E ratio. This ratio reflects the multiple that investors are willing to pay for a share of earnings.

### Forecasting the Equity Risk Premium

To forecast the equity risk premium using the Grinold Kroner Model, we need estimates for next year’s dividend (D1), dividend growth rate (g), and the price-to-earnings ratio (Pi/E1). The dividend growth rate can be estimated by multiplying the retention rate (the proportion of earnings retained) by the return on equity (ROE) (Grinold and Kroner Model for Valuation, 2014). This estimate assumes that companies will reinvest a certain proportion of earnings and generate growth in the future.

By rearranging the equation Pi/E1 = (D1/E1)/(k – g), we can solve for the expected return on the market (k). This expected return, also referred to as the required return, represents the equity risk premium (Dolan, 2023). It reflects the compensation investors demand for taking on the additional risk associated with investing in equities compared to risk-free assets.

### Conclusion

The Grinold Kroner Model provides a useful framework for forecasting the equity risk premium by combining dividend discount models and fundamental factors. By estimating the expected return on the market, investors can gain insights into the relative value of equities compared to risk-free investments. However, it is crucial to acknowledge the inherent uncertainties and limitations associated with forecasting financial variables. Ongoing analysis and monitoring of market conditions are necessary to refine and update forecasts for the equity risk premium.

### References

Grinold and Kroner Model – Breaking Down Finance. (2019, August 23). Breaking Down Finance. https://breakingdownfinance.com/finance-topics/equity-valuation/grinold-and-kroner-model/

Grinold and Kroner Model for valuation. (2014, March 26). Issuu. https://issuu.com/kotaksecurities/docs/grinold_and_kroner_model_for_valuat

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