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Security Analysis and Portfolio Management

SECTION A

“Beta is dead! Long live alpha” Critically assess whether absolute returns are now more

important than relative performance in investment management.

Even though the thought has come up for a while, firm investing returns is becoming more important

recently due to some mutual funds being begun lately with absolute returns targets. Via method of

contrary, the conventional mutual fund wishes to manufacture superior relative investing returns in

comparison to a reasonable standard. The target of absolute returns is to prove margins in the whole time

durations and over a broad variety of market states. Pankin (2008) cited an instance that throughout a

year whilst stocks drop by 10%, a characteristic mutual fund with a relative returns target will be taken

into consideration to have got a great year it gets dropped by just 7%; however that would be bad

absolute returns. Nevertheless, if the market increases by 15% per year, a fund attempting for absolute

returns achieves 10% will be persistent with its target whilst a fund assessed on a relative returns

fundamental with that returns would be taken into consideration to have got bad operation in that year.

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…………………………………………………………………………………………………….

Warren Buffett and his mentor, Benjamin Graham, argued that market risk was less important

than company specific risk in share valuation and investment management. Critically analyse the

basis and evidence for this viewpoint, and its implications

Warren Buffet’s Investment Philosophy

Economic reality, not accounting reality:

Discounted cash flow (DCF):

Opportunity Cost:

Risk-free approach:

Portfolio diversification:

Performance measurement:

Investment strategy:

Corporate governance:

Comparing Warren Buffett’s investment philosophy with the theory of finance

Analyzing and comparing Warren Buffett’s investment philosophy with his investment practices

SECTION B

Q2: Explain why you agree or disagree with the following statements:

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“It is always better to have a portfolio with more convexity than one with less convexity”

It is not always nicer to get a portfolio with being more convex than one being less convex. Even

though with all other stuffs equivalent it is nicer to be more convex than less, the market pays for being

convex in the type of a higher tariff or a lower margin. Yet the advantage of the bigger convexity is

dependent of how much margins vary. As can be understood from the second column of Table 1, if

market profits vary by less than 100 basis marks (more or less), the bullet portfolio, which gets less

convexity, will offer a nicer total returns.

“A bullet portfolio will often outdo a barbell portfolio with the similar dollar period if the

margin curve steepens.”

Q3: Calculate Macaulay’s duration, the modified duration, and the convexity of the following

bonds (annualize the parameters). Assume all of the bonds pay principal at their maturity.

a) Four-year, 9% coupon bond with a principal of £1000 and annual coupon payments trading at

par.

b) Four-year, zero coupon bond with a principal of £1000 and priced at £708.42 to margin 9%.

c) Five-year, 9% coupon bond with a principal of £1000 and annual coupon payments trading at

par.

d) Ten-year, 7% coupon bond with a principal of £1000 and semi-annual coupon payments

(3.5%) and priced at par.

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e) Three-year, 7% coupon bond with a principal of £1000 and semi-annual coupon payments

(3.5%) and priced at par.

f) Three-year zero-coupon bond with a principal of £1000 and priced at £816.30 to yield 7%.

As per the above statistics the input data for the measurement is as follows:

Table 2 Input data

Bond A Bond B Bond C Bond D Bond E Bond F Unit

Payment per year (n) 1 1 1 2 2 1

Coupon (C) 90 0 90 35 35 0 USD

Yield to maturity (y) 0.09 0.09 0.09 0.035 0.035 0.07 %

Maturity 4 4 5 20 6 3 year

Par 1,000 1,000 1,000 1,000 1,000 1,000 USD

Price 1,000 708.42 1,000 1,000 1,000 816.30 USD

Inserting these values into the present value of the coupon payments formula:

Computing the present value of the par or maturity value of $1,000 gives:

1n

M

r

The outcomes get the below observation:

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Table 3 Present value (PV)

t Bond A Bond B Bond C Bond D Bond E Bond F

1 82.5688 0.0000 82.5688 33.8164 33.8164 0.0000

2 75.7512 0.0000 75.7512 32.6729 32.6729 0.0000

3 69.4965 0.0000 69.4965 31.5680 31.5680 0.0000

4 63.7583 0.0000 63.7583 30.5005 30.5005

5 58.4938 29.4691 29.4691

6 28.4725 28.4725

7 27.5097

8 26.5794

9 25.6806

10 24.8122

11 23.9731

12 23.1624

13 22.3791

14 21.6224

15 20.8912

16 20.1847

17 19.5021

18 18.8426

19 18.2054

20 17.5898

Par 708.4252 708.4252 649.9314 502.5659 813.5006 816.2979

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P 1000.0000 708.4252 1000.0000 1000.0000 1000.0000 816.2979

The Macaulay duration is a calculation of the rough shift in rate for a tiny shift in margin.

Macaulay duration =

1 2

1 2

1 1 1 1n n

C C nC nM + +. . .+ +

y y y y

P

Where P = price of the bond, C = semi-annual coupon interest (in dollars), y = one-half the yield to

maturity or required yield, n = number of semi-annual periods (number of years times 2), and M =

maturity value (in dollars).

The observation of the outcomes is illustrated as follows:

Table 4 Value calculated by t*(PV/P)

t Bond A Bond B Bond C Bond D Bond E Bond F

1 0.0826 0.0000 0.0826 0.0338 0.0338 0.0000

2 0.1515 0.0000 0.1515 0.0653 0.0653 0.0000

3 0.2085 0.0000 0.2085 0.0947 0.0947 0.0000

4 0.2550 0.0000 0.2550 0.1220 0.1220

5 0.2925 0.1473 0.1473

6 0.1708 0.1708

7 0.1926

8 0.2126

9 0.2311

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10 0.2481

11 0.2637

12 0.2779

13 0.2909

14 0.3027

15 0.3134

16 0.3230

17 0.3315

18 0.3392

19 0.3459

20 0.3518

Par 2.8337 4.0000 3.2497 10.0513 4.8810 3.0000

Total 3.5313 4.0000 4.2397 14.7098 5.5151 3.0000

The Macaulay duration of listed bonds get the below calculation:

Table 5 Macaulay Duration

Bond A Bond B Bond C Bond D Bond E Bond F

Macaulay Duration 3.5313 4.0000 4.2397 7.3549 2.7575 3.0000

Investors imply to the ratio of Macaulay duration to 1 + y as the modified duration. The calculation is

as below:

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Modified Duration = 1

Macaulay duration

y

The observation of the outcomes is as below:

Table 6 Modified Duration

Bond A Bond B Bond C Bond D Bond E Bond F

Modified Duration -3.2397 -3.6697 -3.8897 -7.1062 -2.6643 -2.8037

It is probably resulting in another formula which does not get the wide measurements of the

Macaulay period and the varied period. This gets accomplished via the rewriting of the rate of a bond

regarding its two elements: (i) the present value of an annuity, in which the annuity is the total of the

coupon payments, and (ii) the present value of the par value. By taking the first derivative and dividing

by P, we achieve another formula for modified period given by:

Modified Duration =

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1001

1 1n n

n C / yC 1

y y y

P

In which the rate with the expression as a ratio of par value.

Bond A Bond B Bond C Bond D Bond E Bond F

Macaulay Duration -3.2397 -3.6697 -3.8897 -3.5531 -1.3321 -2.8037

Double check OK OK OK OK OK OK

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In half years, the convexity measure =Pdy

Pd 1

2

2

. Noting that

2

2

dy

Pd=

3 1 22

( 1) 100 /2 1 21

1 11n n n

n n C yC Cn

y y yyy

,

It is able to insert this amount to convexity portion (half year) formula to achieve:

Convexity Measure (half year) =

3 1 22

( 1) 100 /2 1 21

1 11n n n

n n C yC Cn

y y yyy

1

P

Convexity measure (years) = yearper period min measureconvexity

2

m

The observation of the outcomes are as below:

Table 7 Convexity measure (half year)

Bond A Bond B Bond C Bond D Bond E Bond F

Part 1 24691.36 0.00 24691.36 163265.31 163265.31 0.00

Part 2 0.29 0.29 0.35 0.50 0.19 0.18

Part 3 5777.17 0.00 6625.19 55493.82 26948.26 0.00

Part 4 0.00 1192.53 0.00 0.00 0.00 855.58

Part 5 0.01 0.01 0.01 0.01 0.01 0.01

Convexity measure 14.2221 16.8337 20.1848 257.1992 35.0061 10.4812

Table 8 Convexity measure (in years)

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Bond A Bond B Bond C Bond D Bond E Bond F

Convexity measure 14.2221 16.8337 20.1848 64.2998 8.7515 10.4812

Q4: Given you duration and convexity calculations in Question 3, answer the following:

a) Which bond has the greatest price sensitivity to interest rate changes?

Bond d has the biggest duration and thus gets the biggest rate sensitiveness to interest rate shifts.

b) For an annualized 1% decrease in rates what would be the approximate percentage change in

the prices of Bond d and Bond e?

Employing the modified period, a 1% decline in margins would result in a nearly 7% rise in the tariff

for Bond d and 2.66% rise in tariff for Bond e.

c) Which bond has the greatest non-symmetrical capital gain and capital loss feature?

Bond d has the biggest convexity and thus non-asymmetrical achievement and failure characteristic.

If you were a speculator and expected yields to decrease in the near futures by the same amount

across all maturities (a parallel downward shift in the yield curve), which bond would you select?

It is better to choose bond d - the one with the biggest period; if margins raise, bond d would get the

biggest ratio rise in rate.

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d) If you were a bond portfolio manager and expected yields to increase in the near future by the

same amount across all maturities (a parallel upward shift in the yield curve), which bond

would you select?

It is better to choose bond e – the one with the most minor period; if margins raise, bond e would get

the least ratio decline in rate.

e) Comment on the relation between maturity and a bond’s price sensitivity to interest rate

changes.

The bigger a bond's maturity, the bigger its period, and thus the bigger its rate sensitiveness to

interest prices shifts.

f) Comment on the relation between coupon rate and a bond’s price sensitivity to interest rate

changes.

The less a bond’s coupon price, the bigger its period, and thus the bigger its rate sensitiveness to

interest price shifts.

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References

Alexander Ineichen, C. F. A., CAIA, F., & Keller, T. (2011). Absolute returns and risk management.

Buffett, M., & Clark, D. (2009). Warren Buffett's Management Secrets: Proven Tools for Personal and

Business Success. SimonandSchuster. com.

Buffett, M., & Clark, D. (2011). The Warren Buffett Stock Portfolio: Warren Buffett Stock Picks: why

and when He is Investing in Them. SimonandSchuster. com.

Calandro J.R. (2009). Applied Value Investing. New York: McGraw-Hill.

Ding, B., Shawky, H. A., & Tian, J. (2009). Liquidity shocks, size and the relative performance of hedge

fund strategies. Journal of Banking & Finance, 33(5), 883-891.

Fabozzi, F. J. (2007). Bond markets, analysis and strategies. Pearson Education India

Hou, K., Karolyi, G. A., & Kho, B. C. (2011). What factors drive global stock returns?. Review of

Financial Studies, 24(8), 2527-2574.

Ineichen, A. M. (2002). Absolute returns: the risk and opportunities of hedge fund investing (Vol. 195).

Wiley. com.

Jain, P. C. (2010). Buffett beyond value: Why Warren Buffett looks to growth and management when

investing. Wiley. com.

Lhabitant, F. S. (2011). Handbook of hedge funds (Vol. 579). John Wiley & Sons.

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Pankin, M. (2008). Stock Market Perspective: Absolute and Relative Returns. Available at:

http://www.pankin.com/persp053.pdf

Rajablu, M. (2011). Value investing: review of Warren Buffett's investment philosophy and practice.

Research Journal of Finance and Accounting, 2(4), 1-12.

Reilly, F. K., & Brown, K. C. (2011). Investment analysis and portfolio management. CengageBrain.

com.