Tag Info

11

The PCA analysis does not really tell you what the bonds do but it tells you how the rates move together. The variations of $n$ rates (i.e. 1 y, 2y, ...) are split up in (at first) abstract factors like $$\Delta R_i = \sum_{j=1}^n e_{i,j} f_j$$ where $\Delta R_i$ is the change in the rate $i$ and $f_j$ is factor $j$ and $e_{i,j}$ is the (factor loading=) ...

2

Some models do use ln(r_t), like Black–Derman–Toy and the Black–Karasinski models. Mainly to avoid negative interest rates in low rates / high volatility environments through the use of the log-normal distribution. Negative rates can wreak havoc in option premiums for example. They are interest rates indeed, that we call short rates, not yield on ...

2

If you are not able to find a data set, containing the dividend yield information for all the companies listed in ASX20/50/100/200/300, the only way is for you to make it by researching the companies. However I found this dividend yield scan to get you started. Once you have the dividend yield rate for all the stocks in the given index, it is just a matter ...

2

while it is true that $$\lim_{T\to\infty} Z(t, T) = \lim_{T\to\infty} e^{-r(T-t)} = 0$$ this is when $r$ is independent of time to maturity, a flat and constant yield curve. In practice, we use yield curves which vary depending on what day they are estimated and what maturity the ZCB is. If in fact $r(t, T)$ depends on today and the maturity then the ...

2

This is something that banks don't do very well (in my opinion), but we can look to the insurance industry for help. Insurance liabilities often span decades, and the regulation has come up with something called the Ultimate Forward Rate (or UFR). It's currently a hotly debated topic with the advent of Solvency II (insurance regulation) coming into effect ...

1

First, it's not true that a market sector is cheap whenever the forward curve lies above the par curve. In fact, whenever the yield curve is upward sloping, the forward curve will always lie above the par curve. Conversely, when the yield curve is downward sloping, forwards will always lie beneath the par curve. In the example you quoted, Ilmanen chose a day ...

1

The correct date to use is the Settlement Date, which is one business day after the Trade Date, or in the case of a newly auctioned security, the Issue Date. The Issue Date is typically between T+2 and T+1week for coupon bearing Treasuries. See the Treasury Direct website for examples. The yield function is preferable to the rate function in exceL. ...

1

Happy holidays to you too. The difference is that in one case you hold the bond to maturity (carry) with the Cupon Rate. And the expected return is the YTM (yield) seen on the secondary market trades + the spread. That's it.

1

Have you looked at Quantlib.net? We use it both in the back office and some soft realtime trading system for pricing bonds. There are a few questions on this site that deal with using it for pricing bonds. See here: https://quant.stackexchange.com/questions/tagged/quantlib+bond

1

The time $0$ forward rate from tme $n-1$ to time $n$ is $$1 + i_0(n-1, n) = \dfrac{(1 + s_0(n))^n}{(1+s_0(n-1))^{n-1}}$$ where $s_0(n)$ is the $n$-year spot rate and $i_0(n-1, n)$ is the time $0$ forward rate from time $n-1$ to time $n$. The term structure of interest rates must be increasing to avoid arbitrage opportunities. ...

1

In a case like this, where the settlement date is in the middle of the coupon period, it is not right to use PV = -110 (minus the purchase price) in Step 3. Instead you should increase the purchase price by the accrued interest, which is a fraction of the coupon based on how far the settlement date is within the current coupon period. (So for ex if you are ...

1

The general bond pricing formula for fixed-coupon bonds, assuming settlement on a coupon date, is as follows: $$P = \sum_{i=1}^N \frac{c/f}{(1 + y/n)^{nt}},$$ where $c$ is the size of the cash flow, $f$ is the coupon frequency per year, $y$ is the annualized yield, and $n$ is the compounding frequency per year. In your case, $c$ should be $2.5/2=1.25$. ...

1

Usually yield/time is the standard context for definition of a yield curve, with yields being derived from prices (of interest rate instruments) for certain maturities (times). The investopedia article you are referencing is all about the yield/price connection (since duration and convexity represent first and second order "price" sensitivity measures to "...

1

USGG10Y is the rolling 10-year on-the-run series. On each day, it reflects the yield of the current 10-year on-the-run note. On an auction date, after a new 10-year Treasury is issued, it starts tracking the new 10-year bond yield. The default USGG10Y series is a composite quote from a few dealers. But frankly, given the liquidity and depth of the Treasury ...

1

These are not yield. They are instantaneous short rates which are not directly observable in the market.

1

Simply speaking, return means relative amount of extra money earned after investing of some amount of money: Return = $\frac{Received}{Invested}-1$. If you invested \$100 and received \$100, this means you have zero return (\$100/\$100-1). If you invested \$100 and received \$110, your return in 10% (\$110/\$100-1 = 1.1-1 = 0.1 = 10%). Next step is ...

Only top voted, non community-wiki answers of a minimum length are eligible