Corporate Finance: Essay Quiz Dividend Yield, Capital Gain Yield and Total IRR 03

• 
  Joven industries sold for RM1.90 on 1^st January and ended the year at a price of RM2.50. in addition, the stock paid dividends of RM 0.20 per share. Calculate Joven dividend yield, capital gain yield, and total rate of return for the year.

Answer: 

Given Data

• Beginning Price (P0): RM 1.90
• Ending Price (P1): RM 2.50
• Dividends Paid (D): RM 0.20

1. Dividend Yield

The dividend yield is calculated as follows:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Dividend Yield</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\frac{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">D</span></span>}}{{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0</span></span>}}}$$

Substituting the values:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Dividend Yield</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\frac{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.20</span></span>}}{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1.90</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\approx </span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.1053</span></span>}\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;"> or </span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">10.53</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\%</span></span>}$$

2. Capital Gain Yield

The capital gain yield is calculated using the change in price:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Capital Gain Yield</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\frac{{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0</span></span>}}}{{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0</span></span>}}}$$

Substituting the values:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Capital Gain Yield</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\frac{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">2.50</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1.90</span></span>}}{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1.90</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\frac{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.60</span></span>}}{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1.90</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\approx </span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.3158</span></span>}\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;"> or </span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">31.58</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\%</span></span>}$$

3. Total Rate of Return

The total rate of return combines both the dividend yield and the capital gain yield:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Total Rate of Return</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Dividend Yield</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Capital Gain Yield</span></span>}$$

Substituting the previously calculated yields:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Total Rate of Return</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.1053</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.3158</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\approx </span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.4211</span></span>}\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;"> or </span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">42.11</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\%</span></span>}$$

You earn a total return of -5% on Dolly.com this year, earned -40% last years, and earned 30% two years ago. Calculate both the three year holding period return and the average three year return.

Answer:

To calculate the three-year holding period return and the average three-year return for Dolly.com, we will use the following formulas:

Given Returns

• Year 1: -5%
• Year 2: -40%
• Year 3: 30%

1. Three-Year Holding Period Return

The holding period return (HPR) over multiple periods can be calculated using the formula:

$$\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">H</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">R</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\times </span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">2</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\times </span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">3</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}$$

Where 

$r_1,r_2,r_3$

 are the returns for each year expressed as decimals.

Substituting in the values:

$$\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">H</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">R</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.05</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\times </span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.40</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\times </span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.30</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span>$$

Calculating each term:

$$\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">H</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">R</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.95</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\times </span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.60</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\times </span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1.30</span></span>}$$

Calculating step-by-step:

1. $0.95\times 0.60=0.57$
2. $0.57\times 1.30=0.741$

Now, subtracting 1:

$$\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">H</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">P</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">R</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.741</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">0.259</span></span>}\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;"> or </span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">25.9</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\%</span></span>}$$

2. Average Three-Year Return

The average return over the three years can be calculated using the arithmetic mean of the annual returns:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Average Return</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\frac{{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">1</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">2</span></span>}}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">r</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">3</span></span>}}}{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">3</span></span>}}$$

Substituting in the values:

$$\text{<span style="font-family: verdana; text-align: justify;"><span style="font-size: small;">Average Return</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">=</span></span>\frac{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">5</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\%</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">(</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">-</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">40</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\%</span></span>}<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">+</span></span>\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">30</span></span>}\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">\%</span></span>}}{\mathrm{<span\; style="font-family:\; verdana;\; text-align:\; justify;"><span\; style="font-size:\; small;">3</span></span>}}$$

Calculating step-by-step:

1. Convert percentages to decimals:
   • $-5\mathrm{\%}=-0.05$
   • $-40\mathrm{\%}=-0.40$
   • $30\mathrm{\%}=0.30$
2. Sum the returns:
   $$-0.05+(-0.40)+0.30=-0.05-0.40+0.30=-0.15$$
3. Divide by the number of years:
   $$\text{Average Return}=\frac{-0.15}{3}=-0.05\text{ or }-5\mathrm{\%}$$

• Three-Year Holding Period Return: -25.9%
• Average Three-Year Return: -5%

These calculations indicate that while the average annual return was negative, the holding period return reflects a more significant loss over the three years due to the compounding effects of negative returns in the first two years followed by a positive return in the last year.

• Your portfolios is comprised of 30% of stock R, 50% of the stock S, and 20% of stock T. stock R has a beta of 0.64, stock S has a beta of 1.48 and stock T has a beta of 1.04. What is the beta of your portfolio?

Answer:

To calculate the beta of your portfolio, you can use the weighted average of the betas of the individual stocks in the portfolio. The formula for the portfolio beta (${\beta }_p$) is:

$${\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\beta </span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">p</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">=</span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">w</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">R</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\beta </span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">R</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">+</span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">w</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">S</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\beta </span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">S</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">+</span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">w</span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">T</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\beta </span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">T</span></span>}}$$

Where:

• $w_R,w_S,w_T$ are the weights of stocks R, S, and T in the portfolio, respectively.
• ${\beta }_R,{\beta }_S,{\beta }_T$ are the betas of stocks R, S, and T, respectively.

Given Data

• Weight of Stock R ($w_R$): 30% or 0.30
• Weight of Stock S ($w_S$): 50% or 0.50
• Weight of Stock T ($w_T$): 20% or 0.20
• Beta of Stock R (${\beta }_R$): 0.64
• Beta of Stock S (${\beta }_S$): 1.48
• Beta of Stock T (${\beta }_T$): 1.04

Calculation

Now we can substitute the values into the formula:

$${\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\beta </span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">p</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">=</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">0.30</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">0.64</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">+</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">0.50</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">1.48</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">)</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">+</span></span><span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">(</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">0.20</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\cdot </span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">1.04</span></span>}$$

Calculating each term:

1. For Stock R:
   $$0.30\cdot 0.64=0.192$$
2. For Stock S:
   $$0.50\cdot 1.48=0.740$$
3. For Stock T:
   $$0.20\cdot 1.04=0.208$$

Summing Up

Now add these values together to find the portfolio beta:

$${\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">\beta </span></span>}}_{\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">p</span></span>}}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">=</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">0.192</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">+</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">0.740</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">+</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">0.208</span></span>}<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">=</span></span>\mathrm{<span\; style="font-family:\; verdana;"><span\; style="font-size:\; small;">1.140</span></span>}$$

• What is the difference between systematic and unsystematic risk? Which type of risk is eliminated with well diversified portfolio?

Answer:

The difference between systematic and unsystematic risk is fundamental in understanding investment risks and portfolio management.

Systematic Risk

Systematic risk, also known as market risk, affects the entire market or a significant portion of it. This type of risk is caused by macroeconomic factors that cannot be avoided or diversified away. Examples of systematic risk include:

• Economic recessions
• Changes in interest rates
• Inflation
• Political instability
• Natural disasters

Since systematic risk impacts all investments in the market, it is non-diversifiable. Investors cannot eliminate this risk through diversification; instead, they can manage it through strategies like asset allocation and hedging.

Unsystematic Risk

Unsystematic risk, also referred to as specific or diversifiable risk, is unique to a particular company or industry. This type of risk arises from internal factors that affect a specific organization, such as:

• Poor management decisions
• Product recalls
• Labor strikes
• Competitive pressures

Unsystematic risk can be reduced or eliminated through diversification. By holding a well-diversified portfolio of assets across different industries and sectors, investors can mitigate the impact of any single investment's poor performance on their overall portfolio.

Summary of Differences

• Scope: Systematic risk affects the entire market; unsystematic risk affects specific companies or industries.
• Diversifiability: Systematic risk cannot be eliminated through diversification; unsystematic risk can be mitigated by diversifying investments.
• Examples: Systematic risks include economic downturns and interest rate changes, while unsystematic risks include company-specific issues like management failures or product failures.