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1

After announcement, in December, of the intention to call the bond in April at 11 the market price fell to 11 and apparently remained at 11 throughout January. The broker could have purchased the bond at 11 mid January (no fee or commission) and received back in April a value of 11.15 (i.e. principal plus 6% annual interest chargable for 3 months). The ...


0

One general representation of the CAPM model is to suggest that it is the solution of: $$ \min_w f(w) = \alpha \frac{1}{2}w^T(2\Sigma)w - (1-\alpha)\mu^t w $$ $$ s.t. \quad \delta^T w = 1$$ and different $\alpha$ determine different points on the efficient frontier. Note that this form allows short selling and the solution is closed form. The reformulated ...


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With two changes in the sign of the cash flows, the IRR of the combined cash flows may no longer be unique (there may be two IRRs). You have to be very careful. What I would recommend is drawing the "NPV profile graph" with the NPV on the y axis and different discount rates (0%, 5%, 10%, ..., 35%) on the x axis. The IRRs are the places where the curve ...


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Our paper answers this question in the admittedly simple context of Expected Loss (EL) calculated as the straightforward summation of EAD * PD * LGD from the granular level. EL here is the surrogate for your RWA, and the risk metrics are the granular data (EAD, PD, LGD). The paper proposes how changes in EL can then be attributed / apportioned to changes ...


0

It's pretty close to impossible for anyone to tell you how to pick successful strategies. That's a little like asking 'how do I write a successful novel?" It's equal parts art and science, not to mention informed largely by experience and understanding of the underlying strategy. A couple general comments though: (1) Your Sharpe ratios are quite low. ...


3

This is a quite broad question, but as requested, i would like to provide you four recommendations. First, testing any portfolio sorting-strategy, it is common in academics to account for autocorrelation and heteroscedascitiy in portfolio returns, i.e. applying Newey/West (1987) adjusted standard errors. As you seem to use the R-statistical language, this ...


2

It's best to think of the sum of $da_t A_t$ and $da_t dA_t$: $$ da_t A_t + da_t dA_t = da_t(A_t + dA_t) $$ which is the cost of rebalancing at the new price $A_{t'} = A_t + dA_t$. You don't rebalance the portfolio at $t$ but at $t'$. And the self-financing condition means you need to finance this cost by rebalancing other assets (including possibly the money ...


0

Say you start with 1000 units worth 100 equals value 100,000. You buy 100 more but the price falls to 90, giving you 1100*90 equals 99,000 value. Change in Value = dP * U = -10 * 1000 = -10,000 P * dU = 100 * 100 = 10,000 dP * dU = -10 * 100 = -1,000 The first two, the change in value of existing units, and the value brought in with new purchases ...


2

No, that's right! One fund has a beta of 81.6% and the other 82.4%, each with a ~90% R^2 to market. Therefore, it makes total sense that the spread between the two should have almost no correlation to the market (which is your very low mkt co-efficient value, and your very low R^2). The >90% P-value on the intercept (of the spread) co-efficients does ...


-3

The Boxes I made are monetary even stuff. This is basically what their dealing with.


3

We assume that the price at time $t$ of a zero-coupon bond, with maturity $u$ and unit face value, is of the form \begin{align*} f(u-t, r_t, x_t) = E\left(e^{-\int_t^u r_s ds}\mid \mathcal{F}_t\right). \end{align*} Note that \begin{align*} M(t, r_t, x_t) &\equiv f(u-t, r_t, x_t) e^{-\int_0^t r_s ds} \\ &=E\left(e^{-\int_0^u r_s ds} \mid \mathcal{F}_t ...


3

Classic asset price model in the continuous-time limit using a Wiener process notation can be written as $$ dS_t=\mu S_tdt+\sigma S_t dX $$ where $S_t$ is the stock price (not the stock return) and $dX$ is an independent random variable with normal distribution. If we eliminate the drift ($\mu = 0$) and only focus on randomness as asked in your question we ...


1

For the first question, it is the standard assumption to make for stock returns if no other information is given. That's not to say it's a great assumption, but there it is clearly the only one that can be justified in this context. For the second part, independence of returns tells you that investment for T years has cumulative variance $T \sigma^2$ (when ...


2

The first is something of a theoretical question. It's widely held/assumed that stocks follow a BM process, it appears as though the author is setting the table for the subsequent statement. The second is an artifact of applying Ito's lemma...the $dW_tdt$ and $dtdt$ terms both equal 0, hence fall out, leaving only $dW_t^2$ = dt. Thus, the variance ...


4

I do not think this is allowed in this forum, but anything that has to do with using option implied volatility and skewness to estimate market betas or expected returns. Here's a few references: Measuring Equity Risk with Option-implied Correlations The Skew Risk Premium in the Equity Index Market What is the Expected Return on a Stock? The Term-Structure ...


4

A comprehensive review of how people deal with negative interest rates in SABR / LMM and similar models could make a good thesis.


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Quandl is free for end-of-data data and of very high quality, but intraday is paid. If you need free intraday data (1-minute or 1-hour intervals) you can try firstratedata TickData.com has the highest quality tick-by-tick intraday data but is very expensive and needs to be purchased separately for each ticker symbol.


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