Free online reading

## Table of contents

Abstract

Acknowledgements

i) Introduction

ii) Conceptional and theoretical background

iii) The historical approach

1 Estimation of the historical risk premium for the SSECC

2 Discussion of the results and comparisons to the USA

3 A critical discussion of the historical approach

3.1 Assumptions and problems comprised in the historical approach

3.1.1 Assumptions

3.1.2 Inference testing and time horizon

3.1.3 Risk free security

3.1.4 Arithmetic vs. geometric averages

3.2 Problems occuring through a violation of the assumptions

3.2.1 Bias in data or bias in expectations

3.2.2 Underlying process is nonstationary

4 Assessment of the historical approach for the SSEC

iv) Correcting measures and alternative approaches

1 Correcting measures

2 Risk-return models

3 Surveys

4 Interpretation ol fundamentals

v) Forecasting the risk premium through fundamentals

1 Interpretation of the I’Th ratio

1.1 China’s P/? ratio

2 The implied risk premium ol China

2.1 Forecasting China’s growth rates

2.2 Solving for the implied risk premium

3 Discussion of the implied risk premium

vi) Conclusions

vii) References

Index of tables and figures

viii) Appendix

## Abstract

Despite the great fall of the Shanghai Stock exchange since the beginning of the year 2008, Chinese equities have performed unimaginably during their young history of existence. This paper aims to answer the question whether these returns are sustainable. The equity risk premium probably provides the most powerful tool to do so. Thus, several techniques are presented to estimate its magnitude. It turns out that some techniques are less and others more suitable in an environment of an emerging country. This paper accumulates evidence that investors must be prepared to receive a much lower reward for their investments.

## Acknowledgements

This piece of work would be inexistent without Professor Horst Tomann of the Freie-Universität of Berlin who designated me for the exchange program. I am very grateful to Nick Horsewood who was a good host during the time at the University of Birmingham and gave me a lot of advise. I would like to thank my supervisor Professor Zhenya Liu who suggested the topic and gave me a lot of freedom to design it.

Furthermore, I would like to express my appreciation to Clara Steinmann and Anousheh Alamir for their helpful hands. Pascal Strothmann and Carla Bönhoff for editing my Master Thesis. Last but not least, I thank my grandmother and my parents who never doubted that I would be on the right track but motivated me to reach my achievments.

Responsibilities for any remaining errors lie with me alone.

## i) Introduction

The Shanghai composite reached its highest (6 092 points) on the 16th of October 2007. Since that day the index has fallen and is at about 2 800 points (1st of August 2008) at this moment. Whereas some investors still advertise the market as being a great investment opportunity with high returns, others advise to be careful and consider the market as being overvalued or in a “bubble” that will have to burst eventually. Meanwhile, it is difficult to assess magnitudes of a market value without having an idea what the true value should be. Most economists agree to the fact, that the risk premium is supposed to determine prices and therefore returns of an asset. The risk premium is defined as the difference of returns between a risk free asset and a risky asset. The extra return is required for investors in order to hold risky assets.

Furthermore, it plays an outstanding role in other models. It determines whether projects are undertaken or not (costs of capital), investment policies (of pension funds, investment managers and others) and it is a crucial figure for the government to compensate for regulations.

Despite its recognition and its outstanding role in finance, it is hard to find a consensus about the actual magnitude of the risk premium. Research has mainly been undertaken for the US-American (stock-) market and estimations for that country lie within a span of one percent up to eight percent, highlighting how sensitive the figure is to different assumptions and models. Literature about the risk premium in other countries is rare.

The aim of this paper is to estimate the risk premium of equities in China, represented by the Shanghai Composite. Therefore, I will first have a glance at the historical development of the index, which provided extraordinary returns. This might justify exuberant investors and seduce to the supposition that emerging stock markets deliver high returns at no cost. In contrast to that I explain why historical returns should be treated carefully and why it might be misleading to use them for future forecasts. In a second chapter I discuss advantages and drawbacks of other techniques to estimate equity risk premiums. In a third step I apply a forward looking model to estimate Chinas equity risk premium. It turns out that great returns in the past cannot be expected to be maintained in the near future. Moreover, prices should be considered to be rather too high than too low.

Although other findings should be consulted to deliver the whole picture, this paper provides advice for investors, in giving them an expected return of Chinese stocks. Furthermore, findings can be taken as a benchmark for estimated risk premia in other countries. The magnitude of a risk premium should be assessed in comparison with other available assets. In a globalizing world this can be done by comparing international assets.

## ii) Conceptional and theoretical background

Before proceeding, I would like to give some definitions that are crucial to understand this paper but did not fit into the main text.

In order to motivate investors to hold risky asset, they demand a risk premium. Otherwise they would rather hold a risk free asset, which pays the same return. The riskier an investment, the higher the risk premium should be. The risk premium is the return of the specific asset minus the return of a risk free asset, technically:

illustration not visible in this excerpt^{[1]}

Basically any asset, containing any risk is risky. The risk free asset is compromised, since in reality there is no asset free of risk. However, the risk free asset is usually approximated by an asset that is nearly risk free with equal maturities compared to the risky asset. Since the US treasury department never failed to pay back any deposit, US securities with different maturities are commonly assumed to be risk free.

Furthermore, the questions how risk should be measured remains. Most often they are represented by a statistical figure, measuring a deviation from a reference value (for instance the standard deviation). Markowitz (1952) suggested that the risk should be considered from the view of a well-diversified investor. Hence, only risk that cannot be diversified should be rewarded. Although CAPM models provide a powerful tool of how assets should be priced to each other, the question of how the market portfolio should be priced as whole is difficult to answer. However, there is a clear relationship between the price of the market portfolio and the risk premium or demanded returns. If individuals require a low (high) risk premium to hold risky assets, the price will be relatively high (low). The risk premium is what drives prices and therefore returns. Only in the short run risk premiums and returns can drift apart.

Returns of an asset in turn are defined as price changes (referring to the capital value) plus any cash flows from that asset (direct payments, for instance dividends), hence:

illustration not visible in this excerpt

Fig. 1 comparing US-treasury long-term bonds (T-bonds)^{[2]} and the “Shanghai-Stock-Exchange-Composite” (SSEC), illustrates that aspect^{[3]}. An individual investing $ 1 in long-term government bonds at the beginning of 1926 would have gained about $ 2.50 at the end of 1990. Reinvesting the same amount of $ 2.50 at the beginning of 1991 an individual would have earned $ 6.58 investing in bonds and $45.81 if invested in a portfolio at the SSEC, respectively, until the end of 2007^{[4]}. The wealth path of the SSEC is much more volatile, pointing out the riskiness of this index.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 1 Wealth path of $ 1 invested in long-term bonds at the beginning of 1926 and $2.50 invested in a portfolio at the beginning of 1990, which tracks the SSEC.

## iii) The historical approach

### 1 Estimation of the historical risk premium for the SSECC

A very simple approach to estimate the risk premium is the measurement of its past values. Under the assumption that the data generating process for the risk premium is stationary and unbiased, forecasts can be made by using the historical average value. Accordingly, most written articles about risk premia employ this approach. For the USA the probably most often cited paper is Ibbotson and Sinquefield (1976A). They use data from 1926 until 1974 to estimate the historical equity risk premium for US-stocks.

In the following I estimate the historical risk premium for equities in China. Equities are represented by the “Shanghai-Stock-Exchange-Composite” (SSEC), a value weighted stock index incorporating all A- and B- shares listed at the stock exchange in Shanghai and a market capitalization of about 14.6 trillion Renminbi Yuan or $ 2.1 trillion. The risk free asset is represented by 20 year long-term US-treasury bonds. The USA is the largest single debt issuer in the world, hence this asset is very liquid. However, there has been a discussion to replace T-bonds as a risk free asset during a prolonged budget surplus^{[5]}. To make the indices comparable they are both given in dollar. Both time series are nominal. It is assumed that investors fully anticipate inflation in both countries or that at least expectations are unbiased^{[6]}. The same holds true for uncovered interest parity, hence there is a trade-off between differences in real interest rates and exchange rates movements^{[7]}. Table 2^{[8]} presents data for the two competing asset classes. Arithmetic averages are given for realized returns of bonds, returns of the SSEC, inflation and the risk premium. For the wealth paths geometric averages are employed. Given that data, we can estimate different risk premiums. Taking the whole sample period (until the end of 2007) as the basis for an estimator we obtain a risk premium of 28.4 % (34.19-5.8)^{[9]}. Only taking into account the sample period, which is observable for both indices, we obtain a risk premium of about 24.9 % percent, due to the fact that the bond return from 1991-2007 was above its average. Estimating the risk premium with geometric averages we obtain a risk premium of about 16.34 % (whole sample period) and 12.8 % (18.66-5.86). When integrating data until June 2008, estimations are lowered significantly. For instance arithmetic estimations over the whole period to 26.1 % (31.9-5.8) and geometric averages to 11.4 % (13.75-2.32) and 7.89 % (13.75-5.86)^{[10]}. The results are summarized in Table i.

Table i Estimated risk premiums of the SSEC

illustration not visible in this excerpt

### 2 Discussion of the results and comparisons to the USA

As emphasized above, Ibbotson is doing primary research on the historical equity risk premium in the US. Given the great attention to that data and to keep data up to date, he is issuing an annual yearbook. In the yearbook for 1998 he compared the total return index of the S&P 500 index with US treasury bills and bonds over a time horizon from 1926 to 1998^{[11]}. Statistical values for T-bonds are mainly the same^{[12]} with a yearly average of about 5.6 % and a standard deviation of 9.2 %. Compared to S&P returns with an average of 13 %, this leads to a risk premium of about 7.4 %. The figure is lowered to 5.8 % if geometric averages are employed (11.0-5.2)^{[13]}.

These figures make clear the outstanding performance of the SSEC during its short existence. Despite the drop of the SSEC in 2008, the SSEC still outperformed the S&P 500 by about 19 % (31.9-13) in arithmetic and about 6 % (13.75 +3.13 -11) in geometric terms^{[14]}. However, the standard deviation (risk) was about three times as much (20.9 % for the S&P500).

Having represented both, geometric and arithmetic averages it is difficult to say which of these figures suit the role of an estimator the best. To make a coherent decision it is necessary to know the properties of the market. When assuming that the returns are uncorrelated and we want to forecast the return for the next year, the arithmetic estimator will be the best. However, current literature suggests that returns are mean reverting hence they exhibit autocorrelation. If one assumes that high returns are followed by low returns the geometric estimator might be a better estimator. Then geometric averages must be considered to be determined, but arithmetic averages are dependent on the level of geometric averages and the standard deviation of returns. Hence, the higher the standard deviation, the higher arithmetic averages will be^{[15]}.

illustration not visible in this excerpt

Fig. 2 The graph shows one invested dollar at four different hypothetical interest rates. The magnitude of the interest rates is chosen to approximate historical estimated returns for the four asset classes13: Inflation (3%), T-bonds (5%), S&P ??? (11%) and SSEC (16%)

Nevertheless, both these figures clarify that the risk premium for the SSEC has been incredibly high. One has to keep in mind that a difference of a couple of percentages can make a big difference if compounded over a long time horizon (see fig. 2).

As easy the historical approach may be, as many problems it contains. The next chapter gives a review about concerns with that approach that have occurred in contemporary literature.

### 3 A critical discussion of the historical approach

Asking 226 financial economists what the arithmetic average risk premium would be during the next 30 years, Welch (2000) obtained a mean value of 7.9 %^{[17]}. According to Dimson et al (2003), key finance books at that time were teaching a “normal” risk premium of about 8.5 percent, very close to the figures of the Ibbotson data.

They further suggest that experts might have lowered their expectations to 7.1 %, expecting stock prices to fall after the bull market in the 90s. This suggestion would be reinforced by the fact that they expected the outcome of the survey to be 7.9 %.

Whatever the intuition behind those estimations was, the fact is that the Ibbotson data determined the estimates of financial experts and engaged a lot of articles.

illustration not visible in this excerpt

FIG. 3 Outcomes of the Welch surveys undertaken in 1998 and 2001.

However a “new” stream of literature discovered disadvantages of the historical approach and suggested either techniques to correct them or they suggested different - or just completely new - methods. Influenced by this literature 510 experts in a new survey by Welch (2001) suddenly suggested a figure of 5.5 % for the risk premium^{[19]}.

In the following section I present selected problems comprised in the historical approach which might have induced economists to lower their expectations. Furthermore, I assess the relevance for the SSEC.

#### 3.1 Assumptions and problems comprised in the historical approach

##### 3.1.1 Assumptions

The historical approach works under strong assumptions only. Hence, some authors have argued that the historical approach is inappropriate to make consistent forecasts. Consequently, they have suggested several procedures to tackle these problems. There are two streams, one that has tried to modify the historical approach and one that used completely independent approaches.

Therefore, I discuss conditions under which the historical approach works without difficulty and will relax these conditions successively. As far as possible I refer to techniques that have been developed to overcome these problems.

**[...]**

^{[1]} In the strict sense, this formula holds true if returns are known only, otherwise expectations must be taken into account.

^{[2]} US treasury bonds with a maturity of 20 years.

^{[3]} See Appendix (Table 2) for the figures.

^{[4]} The wealth path holds true, although paid interest in the case of the long term bonds are assumed to be reinvested, whereas the wealth path of the SSEC only takes into account price movements and no dividends(so no returns literally).

^{[5]} Some authors use US-treasury bills rather than T-bonds to represent the risk free asset. They argue that long term bonds are no risk free asset, since they contain inflation risk whereas stocks do not. Nevertheless, they are free of credit risk. Moreover, it is argued that comparisons for long-term investments should be made to a long-term investment vehicle.

^{[6]} If we assume that expectations are formed rationally and unbiased, bond returns should contain the real interest rate & inflation, whereas the risky asset should contain real interest rates + inflation + a risk premium. Hence, inflation should subtract to zero.

^{[7]} Note that exchange rate risk is not eliminated. Exchange rate movements only make up for differences in real interest rates, but not for adverse movements in the price levels. The exchange rate risk premium that investors surcharge for the failure of Power Purchasing Parity is supposed to be measured in the risk premium.

^{[8]} See Appendix

^{[9]} This procedure could be justified if we relax the forgoing assumptions and assume imperfect capital markets. Moreover, it could be assumed that T-bonds and SSEC returns are uncorrelated. However, risk premia are computed of returns, which span the same sample period normally.

^{[10]} The data for 2008 was given weights, since it does not span a whole year. Recalculation of bond returns was neglected, since changes are minor.

^{[11]} The yearbook itself was not available to me, hence, information is taken from Cornell (1999)

^{[12]} This is due to the fact that I use the same data set; only figures from 1998 onwards are added.

^{[13]} Average inflation was close to 3.2 % geometrically and arithmetically.

^{[14]} The SSEC returns contain no dividend payments, whereas the S&P 500 does. Hence, these figures are likely to be underestimated.

^{[15]} See for example Dimson et al (2003)

^{[16]} As much data as available was used. Hence, for the SSEC data since 1990 and for the other asset classes data since 1926. Inflation is no asset literally but implies increasing prices. Hence, tangible goods serve these asset instead.

^{[17]} Figures of the Welch survey are related to T-bills and not bonds.

^{[18]} Figure taken from Dimson et al (2003) and slightly changed

^{[19]} This difference was not caused by new respondents who have not participated in the first survey. Even the “same old” respondents adjusted their estimates downwards.

- Quote paper
- Nano Kurzmann (Author), 2008, China’s Equity Risk Premium, Munich, GRIN Verlag, https://www.grin.com/document/163090

Publish now - it's free

Comments