Sharpe assumed that the return of a security is linearly related to a single index like the market index. 3. Single Index Model Casual observation of the stock prices over a period of time reveals that most of the stock prices move with the market index. When the Sensex increases, stock prices also tend to increase and vice – versa. Sharpe’s SINGLE INDEX MODEL The model has been generated by “WILLIAM SHARPE” in 1963. The Single Index Model is a simplified analysis of “PORTFOLIO SELECTION MODEL” To measure both Risk and Return on the stock. • The SINGLE INDEX MODEL greatly reduces the number of calculations that would otherwise have to be made for a large portfolio of thousands of securities. 4. Sharpe’s Single Index Model and its Application Portfolio Construction 513 1. To get an insight into the idea embedded in Sharpe’s Single Index Model. 2. To construct an optimal portfolio empirically using the Sharpe’s Single Index Model. 3. To determine return and risk of the optimal portfolio constructed by using Sharpe assumed that the return of a security is linearly related to a single index like the market index. It needs 3N + 2 bits of information compared to [N(N + 3)/2] bits of information needed in the Markowitz analysis. Need for Sharpe Single Index Model Single Index Model Stock prices are related to the market index and this relationship could be used to estimate the return of stock.
Sharpe assumed that the return of a security is linearly related to a single index like the market index. 3. Single Index Model Casual observation of the stock prices over a period of time reveals that most of the stock prices move with the market index. When the Sensex increases, stock prices also tend to increase and vice – versa. Sharpe’s SINGLE INDEX MODEL The model has been generated by “WILLIAM SHARPE” in 1963. The Single Index Model is a simplified analysis of “PORTFOLIO SELECTION MODEL” To measure both Risk and Return on the stock. • The SINGLE INDEX MODEL greatly reduces the number of calculations that would otherwise have to be made for a large portfolio of thousands of securities. 4. Sharpe’s Single Index Model and its Application Portfolio Construction 513 1. To get an insight into the idea embedded in Sharpe’s Single Index Model. 2. To construct an optimal portfolio empirically using the Sharpe’s Single Index Model. 3. To determine return and risk of the optimal portfolio constructed by using Sharpe assumed that the return of a security is linearly related to a single index like the market index. It needs 3N + 2 bits of information compared to [N(N + 3)/2] bits of information needed in the Markowitz analysis. Need for Sharpe Single Index Model Single Index Model Stock prices are related to the market index and this relationship could be used to estimate the return of stock.
Sharpe assumed that the return of a security is linearly related to a single index like the market index. It needs 3N + 2 bits of information compared to [N(N + 3)/2] bits of information needed in the Markowitz analysis. Need for Sharpe Single Index Model Single Index Model Stock prices are related to the market index and this relationship could be used to estimate the return of stock. Portfolio Theory- Sharpe Index Model - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. Scribd is the world's largest social reading and publishing site. The construction of an optimal portfolio has become increasingly challenging in recent years, as investors expect to maximize returns and minimize risks from their respective investments. An investor needs to have proper knowledge of security
Sharpe’s Index Model simplifies the process of Markowitz model by reducing the data in a substantive manner. He assumed that the securities not only have individual relationship but they are related to each other through some indexes represented by business activity. This optimal portfolio of Sharpe is called the Single Index Model. The optimal portfolio is directly related to the Beta. If Ri is expected return on stock i and Rf is Risk free Rate, then the excess return = Ri – Rf This has to be adjusted to Bi, namely, are not effective for large , so William Sharpe developed model known as the Single Index Model to simplify the Model is based on the observation that the price of a securities fluctuates in the direction of the market price index. In general, if the stock price index rises then the stock price also rises, and The simplification is achieved through index models. There are essentially two types of index models: Single index model Multi-index model The single index model is the simplest and the most widely used simplification and may be regarded as being at one extreme point of a continuum, with the Markowitz model at the other extreme point. Need for Sharpe Model: Need for Sharpe Model In Markowitz model a number of co-variances have to be estimated. If a financial institution buys 150 stocks, it has to estimate 11,175 i.e. , (N 2 – N)/2 correlation co-efficients. Sharpe assumed that the return of a security is linearly related to a single index like the market index.
Single Index Model and Portfolio Theory Idea: Use estimated SI model covariance matrix instead of sample covariance matrix in forming minimum variance portfolios: min x0Σˆx s.t. x0 ˆ = 0 and x01 =1 Σˆ =ˆ 2 ˆ ˆ0 + Dˆ ˆ=sample means MODEL INDEKS TUNGGAL (Single Index Model) William Sharpe (1963) mengembangkan model yang disebut dengan model indeks tunggal (single-index model). Model ini dapat digunakan untuk menyederhankan perhitungan.