6 votes
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How to compute the yield on the Ultra-Bond Treasury Futures

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=...
JoshK's user avatar
  • 2,613
5 votes
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Campbell Shiller log linear relation

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 ...
Kevin's user avatar
  • 15.7k
4 votes

Does the traditional NPV formula of a cashflow double count risk?

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 $...
Matthew Gunn's user avatar
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3 votes

PV of security with interest-dependent cash flows

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, ...
Kevin's user avatar
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3 votes
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How would this 10s/20s steepener work

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, ...
thetableed's user avatar
3 votes
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MtM of FX Forward

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 ...
dm63's user avatar
  • 17k
3 votes

Rate of convergence between price and value

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 ...
Dave Harris's user avatar
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3 votes
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Bond Fair Value

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.
vanguard2k's user avatar
  • 2,915
3 votes
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Exposure At Default: Calculating the present value

I can see that you provided an answer on your own question, but let me provide the general procedure. We are standing at time $t=0$, we have just issued a loan (bond) with notional $N=1000$ to our ...
Pontus Hultkrantz's user avatar
3 votes
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Calculate interest

You can't derive a formula from this equation to calculate $q$ (or $i$) directly for all values of $n$ given the other variables. However, you can use the RATE() function in Excel (or a similar ...
Alper's user avatar
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3 votes
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Why is NPV a biased measure?

There is no statistical "bias". It is just that NPV and IRR can provide different rankings to projects. For example consider a project with a small initial investment and positive cash flows ...
fes's user avatar
  • 1,717
3 votes

PV different from Dirty Price in QuantLib

It's the combination of two things. First: when passed an interest rate y and a series of coupons paying at dates ...
Luigi Ballabio's user avatar
2 votes

Choice between 2 investments that cost the same but offer different interest and face value

Why don't you calculate the IRR of each investment? (aside from all the issues with IRR).
zglin's user avatar
  • 238
2 votes
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How to calculate the NPV (Net present Value) in this question?

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 ...
ApplePie's user avatar
  • 176
2 votes

How to calculate interest rate in this problem?

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 ...
Liisi's user avatar
  • 21
2 votes
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How to calculate interest rate in this problem?

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 ...
Neeraj's user avatar
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2 votes

How to calculate interest rate in this problem?

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 ...
Alex C's user avatar
  • 9,372
2 votes

Why is PV(tax shield) calculated using cost of debt capital for discounting?

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 ...
nbbo2's user avatar
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2 votes

Characteristics of a Discount Curve

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 ...
Chris Taylor's user avatar
  • 5,901
2 votes

Does the traditional NPV formula of a cashflow double count risk?

“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 ...
David Addison's user avatar
2 votes
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Proof that IRR(A) < IRR(A+B) < IRR(B) ? Ie that the IRR of two cashflows together must be within the range of the IRR of the two cashflows?

Another way to write: IRR(A) = x and IRR(0,0,A) = x is: PV(A;x)=0 and PV(0,0,A;x)=0 where PV=present value, and x is the discount rate. Since we are using the same discount rate x, we can just add ...
dm63's user avatar
  • 17k
2 votes

NPV and efficient market hypothesis

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 ...
Philipp S's user avatar
2 votes

Expected return rate greater than required return rate

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'...
AllBlooming's user avatar
2 votes
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NPV of Future Investment: Two Approaches?

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=\...
fes's user avatar
  • 1,717
2 votes

Is the $NPV$ always a decreasing function in $r$

Try $f_0=-0.9975, f_1=2.9975, f_2=-3, f_3=1$. This should have 3i IRRs, namely -5%, 0 and 5% with the desired behavior between about -3% and +3%.
dm63's user avatar
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2 votes
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Closed-form solution for the PV of these cash flows

Cool question! In the following, I first use the fact that cosine of $\frac{\pi}{2}i$ is zero for odd numbers. I then rewrite $\cos(\pi i)$ as $(-1)^i$. Then, I add the zeroth term, apply the well-...
Kevin's user avatar
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2 votes
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Value of the logcontract $Q^T(t,S)$ with payoff $Q(T,S)=-2lnS_T$

In the Black-Scholes model, risk-neutral the dynamics of $S_t$ are given by $$ dS_t = (r-q)S_t dt + \sigma S_t dW_t. $$ Using Itô's lemma, we can find the dynamics of the log-process $$ d\log S_t = \...
Achrbot's user avatar
  • 178
1 vote

Campbell Shiller log linear relation

The second expression is just another representation of the former and has nothing to do with continuous compounding. Instead note that $\log(a)-\log(b)=\log\left(\frac{a}{b}\right)$ from which the ...
sp59b2's user avatar
  • 197
1 vote

NPV and efficient market hypothesis

Note that CF1 is a weighted average of possible future outcomes, about which it is possible for different investors to have different beliefs and risk preferences. NPV = -I + sum(p(i) * CFi1) /(1+k) ...
demully's user avatar
  • 5,071
1 vote
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How does one calculate the duration of a cash flow

Let's consider a single cash flow CF $PV = (\frac{1}{1+i})^n CF$ As you wrote $v = -\frac{1}{PV} \frac{d PV}{di}$ Taking the derivative of PV with respect to i and plugging it in: $v= - \frac{(1+i)...
Alex C's user avatar
  • 9,372

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