Question

The five largest tech companies (Google, Apple, Facebook, Amazon, Microsoft or GAFAM) now make up 20% of the S&P 500 (the market portfolio). This problem aims to quantify the consequence of this increasing concentration for investors.

We assume that the entire security market is made of only three types of assets: a risk-free asset (rf = 3%) and two risky securities G (a portfolio composed by investing in the five GAFAM stocks) and B (a portfolio composed by investing in the rest of the S&P 500, i.e., it is composed of 495 different stocks). You can think of G and B as stocks.

There are 500 shares of G is worth $10 per share, and 10,000 shares of B worth $2 per share. G and B both generate expected returns equal to 7%. The volatility of G is equal to 22.6% and the volatility of B is equal to 5.9%. The correlation of the returns of G and B is equal to 0.76.

1) One of your friend thinks that he’s not affected by the increasing role of the GAFAM, and that it is still possible to find a feasible portfolio with a return of 6% and a volatility lower than 6% What do you tell him? Show that the maximum value for the volatility of the market portfolio for this type of portfolio to be implementable in practice is 8%. Would it have been feasible to implement such a portfolio if G was worth $2 per share? Hint: According to the CAPM, which strategies yield the best return-volatility ratio?

Answer 1

This question has to be answered on the basis of volatility that is reward to volatility which is commonly referred to as sharpe method or sharpe ratio the higher the ratio better it is.

Formula used=

Rp-Rf/ơp

Rp=Return of portfolio

Rf=Risk free asset

Ơp=Standard deviation stated in this question as volatility

Step1

It is important to know the weight of stocks

As stated GAFM referred as G is 20%

S&P referred to as G =80%

Lets check:

Stock G = 500 shares×10 = $5,000

Stock B = 10,000shares ×2 = $20,000

Total value of portfolio = $25,000

Weight Of B (495 stocks) = (20,000÷25,000)×100 = 80%

Weight of G which represents GAFAM stocks = 20%

Now volatility shows which stock is riskier hence G seems to be riskier than B

Step2 Show that the maximum value for the volatility of the market portfolio for this type of portfolio to be implementable in practice is 8%.?

Volatility Can be calculated: asfollows

volatility of portfolio

√(Weightof stock G)^2 × (volatility of stock G)^2 + (Weightof stock B)^2 × ( volatility of stock B)^2 + 2 × Weight of stock G × Weight of stock B × volatility of stock G × volatility of stock B × correlation coefficient of stock G and B

√( 0.20)^2 × (22.6)^2 + (0.80)^2 × (5.9)^2 + 2 × 0.20 × 0.80 × 22.6 × 5.9 × 0.76

= √ 0.04 × 510.76 + 0.64 × 34.81 + 32.43

= √ 20.4304 + 22.2784 + 32.43

= √ 75.1388

= 8.67%

Hence it is 8.67%

hence you can consider a round off to 8% however lets take it 8.67% for accurate calcualtion

Step 3

Would it have been feasible to implement such a portfolio if G was worth $2 per share? Hint: According to the CAPM, which strategies yield the best return-volatility ratio?

It is important to find sharpe ratio to know

reward to volatility of PORTFOLIO

Re=7%(given return)

Rf=3%(given risk free return )

(0.07 - 0.03) ÷ 0.0867 ]×100

= [0.04 ÷ 0.0867]×100

= 46.14%

Hence if Stock g is worth $ 2

Stock of G = 500×2 = $1,000

Stock of B = $20,000

Total value = $21,000

Weight of stock G = 1,000÷21,000 = 4.76%

Weight of stock B = 100 - 4.76 = 95.24%

correlation=0.76 (given)

Volatility of risky portfolio:

= √( 0.0476)^2 × (22.6)^2 + (0.9524)^2 × (5.9)^2 + 2 × 0.0476 × 0.9524 × 22.6 × 5.9 × 0.76

= √ 0.00226 × 510.76 + 0.9071 × 34.81 + 9.1882

= √ 1.1543176 + 31.576151 + 9.1882

= √ 41.9187

= 6.47%

Return to volatility ratio

= [(0.07 - 0.03) ÷ 0.0647]×100

= (0.04 ÷ 0.0647)×100

61.82%

Step4 One of your friend thinks that he’s not affected by the increasing role of the GAFAM, and that it is still possible to find a feasible portfolio with a return of 6% and a volatility lower than 6% What do you tell him?

Now again use sharpe ratio

Rf=3%

Re=6%

Volatility=5% (lower than 6% assume 5%)

=6-3/5=0.6

=60%

Volatility=4% (lower than 6% assume 4%)

75%

Analysis: in comparision to the volatility of portfolio 46.7% if expected return is 6% and volatility is lower than 6% yes it is possible to find a feasible portfolio as reward to volatility ratio is higher than portfolio’s reward to volatility.

I request Please ask any doubt i will explain.Thank you Good Luck.