本項研究企圖嘗試以南非的FTSE / JSE前40指數成份股，合併三因子模型來預測國家風險溢價的準確度。有六種投資組合的結構遵循三因子模型理論（ 2003年） 。推算的數據是從2007年7月至二2014年11月。除了三因子模型，我們也增加了國家風險溢價的評估。估計方法是國家違約價差(Country Default Spread)，其次是Damodaran（ 2013年） 。
由三因子模型（1993）的預測，我們發現2007年7月至二2014年11月期間小資本額股市(small market cap stocks)表現優於大資本額股市(big market cap stocks)，平均每月模擬组合收益率SMB (Small minus big)約為1.41 ％和16.90 ％ （年度） ;價值股也獲得了平均比成長股更高的收益的平均溢價HML約為1.69 ％和20.25 ％ （每年） 。在此期間（ R_m - R_f）的平均市場風險溢價已經被認為是0.07 ％ （月）和0.88 ％ （年度） 。
利用債券價差給出了南非與2.04 ％的高國家風險溢價，而基於這兩個國家違約價差(Country Default Spread)（ CDS ） ，並評價/風險分數估計分別給予1.77 ％和1.75 ％ 。假設美國和其他成熟股票市場的總股權風險溢價為5.48 ％ ，是5.48 ％ + 2.04 ％ = 7.52 ％或5.48 ％ + 1.77 ％ = 7.25 ％或5.48 ％ + 1.7%南非的風險溢價 = 7.23 ％ 。
本篇研究的結論係:與這兩個在約翰內斯堡證券交易所和資本估計，在南非的金融市場的成本KPMG南非的研究報告中的財務風險服務基本一致。
關鍵詞：三因子模型, 國家風險溢價,債券價差, 國家違約價差

The main objective of this study is to estimate the stocks returns of the South African’s FTSE/JSE top 40 index, using the Fama French Three Factor model and the country risk premium approach. The construction of the six size portfolios followed the same process in Fama and French (1993). The period for the estimation spans from 07/2007 to 11/2014. In addition to the three factor model, we added a country risk premium’s estimation value. The estimation approach which is the Country Default Spread, followed Damodaran (2013).
As Fama and French (1993) predicted, we found that for the period 07/2007 – 11/2014 the small market cap stocks outperformed the big market cap stocks. The average monthly premium (SMB) was about 1.41% and 16.90% (annually). Value stocks also have earned on average higher returns than growth stocks. The average monthly premium HML was about 1.69% and 20.25% (annually). The average market risk premium over the period (R_m-R_f) has been found to be 0.07% (monthly) and 0.88% (annually).
Using the bond spread has given a high country risk premium for South Africa: 2.04 %, while both the Country Default Spread (CDS), and the rating/risk scores based estimates gave 1.77% and 1.75% respectively. The total equity risk premium for the United States which is a mature equity market was 5.48% in November 2014. The risk premium for South Africa can be computed as 5.48 % + 2.04 % = 7.52% or 5.48 % + 1.77 % = 7.25 % or 5.48 % + 1.75 % = 7.23 %. The empirical results are approximately consistent with both the Financial Risk Service on the Johannesburg Stock Exchange’s estimation and KPMG South Africa’s report on the cost of capital estimation in the South Africa’s financial market.
Key word: Fama French-Three Factor, Country Risk Premium, Bond Spread, Country Default Spread, Equity risk premium

CONTENTS
摘要 ii
Abstract iii
I. INTRODUCTION 1
1.1. Background 1
A. South Africa presentation 4
1.2 Motivation for Research and Contribution 6
II. THEORETICAL BACKGROUND AND LITERATURE REVIEW 9
2.1 Cost of Equity 9
2.2. The Capital Asset Pricing Model (CAPM) 9
2.3. The Fama French Three-Factor Model (FF3FM) 10
2.4. Literature review 11
III. RESEARCH METHODOLOGY AND DATA 19
3.1. Portfolios construction and Data 24
3.2. Empirical results 26
3.2.1. The historical prices, the monthly risk free rate, and the market premium computation results 26
3.2.2. Explanation of the six size portfolios’ returns 26
3.2.3. Explanation of the SMB and HML results 27
3.2.4. Interpretation of the three-factor portfolios ’correlation 29
3.2.5. The CAPM regression result (see appendix table 3.12) 31
3.2.6. The three-factor regression’s result (see appendix table 3.14) 33
IV. COUNTRY RISK PREMIUM 35
4.1. Theoretical Background of the Country risk premium 35
4.2. Estimating a Country Risk Premium 36
4.2.1 Historical Premium Plus 36
4.2.2. South Africa country risk premium estimation 42
V. DISCUSSION, SUMMARY RESULTS AND CONCLUSION 46
5.1. Cost of Capital and Impairment Testing 2012 by KPMG South Africa 46
5.1.1. Sample survey 46
5.1.2. Determination of the cost of capital 46
5.1.3 Cost of capital parameters 47
5.2. Discussion 51
5.3. Conclusion 52
REFERENCES 57
APPENDIX 61

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