Fight Finance

(a) The internal rate of return (IRR) of buying a fairly priced bond is equal to the bond's yield.

(b) The Present Value of a fairly priced bond's coupons and face value is equal to its price.

(c) If a fairly priced bond's required return rises, its price will fall.

(d) Fairly priced premium bonds' yields are less than their coupon rates, prices are more than their face values, and the NPV of buying them is therefore positive.

(e) The NPV of buying a fairly priced bond is zero.

(a) Premium bonds have a positive expected capital return.

(b) Discount bonds have a positive expected capital return.

(c) Par bonds have a zero expected capital return.

(d) Par bonds have a total expected yield equal to their coupon yield.

(e) Zero coupon bonds selling at par would have zero expected total, income and capital yields.

(a) 2.7355

(b) 2.3596

(c) 1.7355

(d) 1.2645

(e) 0.2645

(a) 1: short call, 2: long call, 3: short put, 4: long put.

(b) 1: long call, 2: long put, 3: short call, 4: short put.

(c) 1: short put, 2: long put, 3: short call, 4: long call.

(d) 1: long put, 2: short put, 3: long call, 4: short call.

(e) 1: short call, 2: long put, 3: long call, 4: short put.

(a) -1

(b) -0.5

(c) 0

(d) 0.5

(e) 1

(a) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(b) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(c) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^4} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##

(d) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{10}{(1+0.1)^6} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##

(e) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^3} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(a) 77.6034%

(b) 30.3779%

(c) 28.8603%

(d) 22.3966%

(e) 7.5304%

(a) Green is a stock's continuously compounded rate of return, also called the log gross discrete return. ##r_\text{cc} = \ln(P_1/P_0)##

(b) Blue is a stock's future price, ##P_1##

(c) Blue is a stock's gross discrete return. ##\text{GDR} = P_1/P_0##

(d) Blue is a stock's effective rate of return. ##r_\text{eff} = (P_1-P_0)/P_0##

(e) Red is a stock's net discrete return. ##\text{NDR} = \text{GDR}-1##

(a) Buffett is clever and by reading the news and financial reports he is able to buy under-priced stocks and sell over-priced stocks. This provides evidence for rejecting the semi-strong and strong form EMH.

(b) Buffett was lucky, his strategy happened to be the right one, not due to its merits, just by chance. This provides no evidence for or against the weak, semi-strong or strong form EMH.

(c) Buffett’s investment strategy exposes investors to higher undiversifiable risk than the market and therefore deserves a higher return. This provides no evidence for or against the weak, semi-strong or strong form EMH.

(d) Buffett is an insider trader and is able to make money from his private information. This provides evidence for rejecting the semi-strong and strong form EMH. (Note: Warren Buffett is not an insider trader, he is an honest philanthropist, but assume the contrary in this answer option).

(e) Buffett may not have beaten the market because the graphs ignore dividends - the S&P500 is the price index rather than the accumulation index and BRK pays no dividends, so even though BRK has a higher capital return than the S&P500, the total returns could be equal. This provides no evidence for or against the weak, semi-strong or strong form EMH.

(a) Best day of the 5% worst days’ results.

(b) Worst day of the 5% worst days’ results.

(c) Best day of the 5% best days’ results.

(d) Worst day of the 5% best days’ results.

(e) Best day of the 95% worst days’ results.