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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=) ...


The main problem is that you cannot achieve Libor in the markets. So the old-fashioned method of discounting at Libor doesn't work any more. As an example, if you compound up the 3m Libor with today's price on a 3x6 FRA, you won't get 6m Libor. Traditionally, that would mean arbitrage, but these days it's just a fact of life. You cannot achieve 3m Libor for ...


The rate is the return on your investment. Since you'll receive 100\$ after 12 months, $\frac{100 - P}{P} = \frac{100 - 89.0}{89.0} = \frac{11}{89} = 12.36 \%$. Same for the 6-month T-Bill: $\frac{100 - P}{P} = \frac{100 - 94.0}{94.0} = \frac{6}{94} = 6.38 \%$.


Strictly speaking, any risk-free interest rate can be composed into three components: The rate expectations component is the market's "true" expectation for future interest rate. A bond risk premium component: longer maturity bonds have higher duration risk than cash. Accordingly market participants will demand more compensation for taking on duration ...


Do you want to model the returns in a risk-neutral framework (for derivatives) or in the real world measure (for risk analysis/portfolio construction)? For the first approach (say modelling under $Q$) you should go to the literature on bond and FX-derivatives. I would go more into detail if this is your aim. The formulation $N(\mu-\sigma^2/2,\sigma)$ ...


If a bank lends 6m Libor and finances it by borrowing 3m Libor and borrowing forward 3x6 libor, this is not arbitrage, as the bank is assuming 6m credit risk whilst his financing is 3m credit risk. (There are also other factors like regulatory capital, tying up balance sheet for 6m, etc.) So the text book case where the 3x6 FRA (or front Eurodollar) is equal ...


1) JPY yield curve is currently upward sloping, not inverted... 2) Empirically, an upward sloping yield curve predicts recessions, not an inverted one. See this famous paper http://newyorkfed.org/research/current_issues/ci2-7.pdf

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