Assignment #01 Marks = 20

Portfolio Risk and Return Analysis Diversification is considered as a key to reduce portfolio risk. Investors and portfolio managers try to construct an efficient portfolio with an aim to maximize return by keeping the risk at

minimum level. In this process, the decision to include any security in a portfolio depends on many factors, among which risk and return of securities are at top. Along with risk and return of individual securities, it is also important to consider the correlation among portfolio securities as

the key to diversification is to add un-correlated or negatively correlated securities in the portfolio that can help in reducing the risk. Considering this information about diversification and portfolio construction, you are required to construct equally weighted portfolios of two securities with all possible combination of securities. From the market analysis, following information is available about three securities:

Security A’s expected return | 15% |
---|---|

Security B’s expected return | 16% |

Security C’s expected return | 10% |

Market return | 15% |

Risk free rate of return | 12% |

Market Beta | 1 |

Requirements:

- List down all possible portfolios consisting of different combination of 2 securities.

Hint: Portfolio 1 = Security A + Security B - Calculate expected return for each possible portfolio.
- Calculate beta for each possible portfolio (calculation of individual stock betas is also

mandatory). - Identify the portfolio that is riskier than market.

NOTE: Formula and calculations are mandatory in each part as these carry marks.

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Answer 01: List down all possible portfolios consisting of different combination of 2 securities.

Portfolio 01: Security A + Security B

Portfolio 02: Security A + Security C

Portfolio 03: Security B + Security C

Answer 02: Calculate expected return for each possible portfolio.

Portfolio 01: Security A + Security B

According to data,

Value Expected rate of return

Security A 50% 15%

Security B 50% 16%

rP = (rA x A) + (rB x B)

rP = (50% x 15/100) + (50% x 16/100)

rP = 7.5% + 8%

rP = 15.5% (Expected rate of rate for Portfolio 01)

Portfolio 02: Security A + Security C

Value Expected rate of return

Security A 50% 15%

Security C 50% 10%

rP = (rA x A) + (rC x C)

rP = (50% x 15/100) + (50% x 10/100)

rP = 7.5% + 5%

rP = 12.5% (Expected rate of rate for Portfolio 02)

Portfolio 03: Security B + Security C

Value Expected rate of return

Security A 50% 15%

Security C 50% 10%

rP = (rB x B) + (rC x C)

rP = (50% x 16/100) + (50% x 10/100)

rP = 8% + 5%

rP = 13% (Expected rate of rate for Portfolio 03)

Answer 03: Calculate beta for each possible portfolio (calculation of individual stock betas is also mandatory).

–> Risk free rate = 12%

–> Market rate = 15%

Beta for Individual stocks:

Beta for Security A: security A rate of return - risk free rate

15% - 12% = -3

Market rate – risk free rate of return

15% - 12% = 3

Beta for security A = 3/3 = 1 (Beta for Security A)

Beta for Security B: security B rate of return – risk free rate

16% - 12% = 4

Market rate – risk free rate of return

15% - 12% = 3

Beta for security B = 4/3 = 1.33 (Beta for Security B)

Beta for Security security C rate of return – risk free rate

10% - 12% = -2

Market rate – risk free rate of return

15% - 12% = 3

Beta for security C = -2/3 = -0.66 (Beta for Security C)

Calculate expected return for each possible portfolio.

Calculating Expected 2-Stock Portfolio Return & Risk Expected Portfolio Return =rP * = xA rA + xB rB Portfolio Risk is generally not a simple weighted average. Up to this point we only look at the portfolio which has only two stocks. Interpreting 2-Stock Portfolio Risk Formula:

From where you read teh terms “Middle” and High Portfolio?

A portfolio is a collection of different securities owned by an investor or institution. For example a portfolio may consist of stock, bonds and T-bills and within that portfolio there can be stocks and bonds of different companies. Portfolio is constructed to diversify risk attached with different investment. To minimize risk securities from different industries are added in the portfolio so that loss of one security may be compensated with the profit of other.

]]>X is Investment weight of specific stock in the total value of the Portfolio. Your example has been taught in details with each step in lecture 21. It seems you did not watch the video lecture number 21, so you must watch it carefully and practice its content with some hypothetical data to grip the concept. ]]>

Portfolio

A.o.A sir,

Portfolio Risk - Example Recap

Complete 2-Stock Investment Portfolio Data:

Value (Rs) Exp Return (%) Risk (Std Dev)

Stock A 30 20 20%

Stock B 70 10 5%

Total Value = 100 Correlation Coeff Ro = + 0.6

2-Stock Portfolio Risk Calculation:

= √ x2 σA2 + xB2 σ2 + 2 (XA XB σA σB ρ AB)

A B

= {0.0036 + 0.001225 + 0.00252} 0.5 = 0.0857= 8.57%

• 2-Stock Portfolio Return Calculation:

rP* = x A r A + x B r B = 6 + 7 = 13%

Sir pls explain what value should we put for X in above formula. Further pls >provide this example solution in detail by adding more steps and values one >by one. As in this example, after formula directly answer is given. It has not >been explained what value is put for X and others. Moreover, is it necessary >to put * on P for calculating Return. Pls also explain what Ro stands for.

A.o.A sir,

Sir in my last message, values of formula are disrupted due to format error, but this formula is the one that is mentiioned in lecture 22. So please explain it as per lecture 22 data.

Moreover, u have replied to the student who raised question after me, but my question solution is still awaited.

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