4

I think you have a little misunderstanding about treasury futures. I would get this book: http://www.amazon.com/Treasury-Bond-Basis-Depth-Arbitrageurs/dp/0071456104?ie=UTF8&psc=1&redirect=true&ref_=oh_aui_search_detailpage It is the absolute best guide to this product. A few important things to understand: Every treasury future has ...


4

You can simply start with the definition of gross returns \begin{align*} R_{t+1}&=\frac{D_{t+1}+P_{t+1}}{P_t} \\ &=\frac{1+P_{t+1}/D_{t+1}}{P_t/D_t}\frac{D_{t+1}}{D_t}, \end{align*} where the first fraction contains now your price dividend ratio. Going to log-returns, \begin{align*} r_{t+1} &= \ln\left(1+\frac{P_{t+1}}{D_{t+1}}\right) - \ln\left(\...


3

You are correct on both questions. 1 you answered yourself. It is the correct rate to close out the trade. 2 you use a dollar discount rate because you are discounting dollars. The (1-K/X) term represents one dollar from the first trade and K/X dollars from the close out trade.


3

I performed spectral analysis on the stock market for disaggregated returns. If $\mu$ is the center of location and anything away from $\mu$ is an "error", then the stock market is in equilibrium once every 20-21 years as an aggregate whole. But, like a musical instrument, the periods of the individual firms could be relatively small. Still, that would ...


3

That formula is algebraically equivalent to saying different, stochastic assets can have different expected returns. $$ \mathbb{E} \left[ R_i \right] = r_f + \gamma_i $$ Some simple algebra Let $X_i$ be a random variable denoting a risky cash flow, $p_i$ be today's price of that risky cash flow, $r_f$ be the risk free rate, and $\gamma_i$ be some risk ...


3

You have to discount the future cash flows with your discount rate (= yield) The coupon is paid quarterly, yet you discount annually. You will miss all other coupons in your calculation.


3

As long as your market is complete and $\tau$ is measurable w.r.t. the filtration generated by the market the continuous cash flow paid until $\tau$ is a hedgeable contingent claim and you have to work under the risk neutral measure.


3

Carry is typically only associated with known cashflows - its closely related cousin, roll, is typically associated with unknown cashflows, assuming the state of the world is unchanged. Given this, carry is typically only analyzed for the current period of the swap or bond. If we assume your swaps are fixed Semi vs a 6m Ibor index, then the natural period ...


3

If the cash flows depend on the (random) interest rates, then the $C_i$ are random variables and so would be the sum $\sum\limits_{i=1}^n C_id(i)$. However, initial market prices need to be constants, they cannot be random (because you need to know how much this claim is worth right now). The $d(i)$ are real numbers though since they are discount factors (...


2

Why don't you calculate the IRR of each investment? (aside from all the issues with IRR).


2

I have laid out below one way of solving this kind of problem. You have your timeline right and I have reproduced it with the correct amounts. The way to discount your 30Ks is the same as discounting 1,500K if you do it this way. Basically, you need to compute a discount factor. To calculate this discount factor, you need to de-annualize your interest rate ...


2

you can also solve this by using the PMT function and goalseek in excel. The answer is as follows: What I did is, I first set the interest rate to 0% and calculated the monthly payment using the PMT function. Then I goalseeked the monthly interest rate such that the monthly payment would be 300.


2

The annuity expression $a_{4}^{(12)}$is written as: $$a_{4}^{(12)}= \frac{1-(1+i)^{-4}}{i^{(12)}} = \frac{i}{i^{(12)}} a_4$$ where, $i$ is the effective annual rate of interest and $i^{(12)}$ is nominal rate of interest convertible monthly, which is equal to $$i^{(12)}=12((1+i)^{1/12}-1)$$ There is no closed formula to get the interest rate, you have to ...


2

There are 48 monthly payments. You can use the formula for the Present Value of an annuity: $12000 = 300 \frac{1}{i/12}[ 1-\frac{1}{(1+i/12)^{48}}]$ to find the interest rate However there is no explicit solution for i, it is solved by trial and error. The value I get is 9.2418%


2

Pricing always takes place under the risk neutral probability measure. In fact, this would make the price more conservative (i.e. lower) with respect to risk; if you priced it under the true measure you would be putting a smaller hazard rate for this random time. Completeness make the risk neutral probability measure unique. In your case you might have ...


2

We are comparing two situations: (1) an all equity firm, versus (2) the same firm which has decided to do a predefined amount of borrowing. Because the tax shields arise as a result of the borrowing decision (i.e. they are a potential advantage of borrowing) they are discounted at the borrowing rate. It is treated almost as a separate project: to borrow ...


2

By no arbitrage, market participants need to agree on the values of the discount factor, even if they are using different conventions (day count, compounding period) to convert the discount factor into a rate. For example, consider two discount factors computed using continuous compounding, where one is computed using the 30/360 day count (year fraction $t_{...


2

The conversion factor associated with each bond the futures' delivery basket is constructed such that the invoice prices of the bonds are identical under the assumption that the yield curve is flat at the level of the futures' notional coupon. Therefore, the bond with the highest duration will be the CTD when yields are above the notional coupon and the bond ...


2

First, I am not sure which exact statement was made. Also, you cannot just say "without CF" because you are essentially creating an artificial market with messed-up utility. In summary the cheapest-to-deliver bond is: The bond that results in the smallest loss or greatest profit for the futures seller. Futures sellers have to buy the bonds they are going ...


2

The assumption that the discount rate should be derived from the IRR of an alternative investment is not correct. Commonly the WACC of the company (or the WACC of the funds needed for the investment if it is standalone) is used. If this is not available, you could make use of a combination of publicly available rates and some risk-adjustments: risk-free ...


2

The proper way is to discount each and every single item of cash flow (the initial $50,000 "grant" as well as the 10 individual interest payments) each one at the discount rate of 4%. In numbers, it's quite a big difference between the two methods, as shown in this table: If you discounted just the ending capital - as suggested by you - you would ...


2

Assume you apply a constant discount rate $\rho$ to your risky payoff and discount rate $\delta$ to riskless payoffs. The time $t$ value of your payoff stream is $$\int_t^{\infty}R_se^{-\rho (s-t)}ds=\frac{R_t}{\rho-\mu},$$ where you need $\rho > \mu$. Within this framework the time $0$ value of your investment is $$\frac{R_te^{-\delta t}}{\rho-\mu},$$ ...


1

I do not follow your analysis. In the case of either type of annuity the FV is equal to the PV times $(1+r)^n$. This factor is simply the factor which translates any amount in period 0 into an equivalent amount in period n. For an ordinary annuity: $$PVA=PMT \frac{1}{r}[1-\frac{1}{(1+r)^n}]$$ When this value is "transferred" to period $n$ by multiplying ...


1

“You can't compensate for risk by using a high discount rate." - Warren Buffett at the 1998 Berkshire Hathaway Shareholder Meeting The simple answer to your question is, “yes, many implementations of discounted cash flow analyses which adjust the discount rate for risk are double counting”. This practice is pervasive in academia, but has no basis in the ...


1

In Wolfram Alpha language ... 2.7∗10^6*(1+x)^12 -75000*(1+x)^8 +50,000 -3.1∗10^6 = 0 ... gives x≈0.0124671 per month, which is 16.03% per annum. I.e. All incomings and outgoings must add up to zero, after adjusting for the monthly interest rate "x" over the number of months invested. 2.7m remains in the fund for the full 13-1 = 12 months, and would ...


1

Yes, the IRR is the same regardless of the prepayment date. The only thing that varies is the life of the loan.


1

Your thought process on valuing the tax savings to the whole enterprise at the cost of capital makes perfect sense to me. While I get the thought process on tax savings being funded by debt, the cash flows due to tax savings do not flow back to debt, but rather to the enterprise whether or not the firm is highly leveraged. I think a simple scenario ...


1

I know this question has been answered but I am giving a complete derivation to assist others as well as serve as my notes. We will take a firm with a free cash flow $\mathcal F$ every year perpetually. This is a simplification that can easily be generalized to variable payments. Unlevered Firm The earnings by the stockholders are reduced by taxes. Thus ...


1

So, you have this: $$ \sum_{k=1}^{k=15} 0.8 \cdot 1.06^{2k} = 5.3456\ldots $$ And you want to know if there's a formula, or closed form. Yes there is. $$ \sum_{k=1}^{k=n} x^{k} = x \frac{x^{n+1}-1}{x-1} $$ Where, we're going to set $x=1.06^{-2}$, and sum from 1 to 15 (since you're not including the first period in the valuations). $$ 0.8 \sum_{k=1}^{k=...


1

In basic instruments, one can ignore the past fixings and price purely on the future cashflows. Hence the term Net Present Value. With more exotic stuff such as range accruals, the past fixings are used to calculate the future payoff. In this case, to find the NPV at an intermediate date between the start date and expiry, you typically need to enter the ...


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