Beta vs. duration

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old_akakaraka

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Somehow the whole equity/beta and FI/duration framework does not make sense to me when comparing the different parts of the curriculum:
- From the institutional PM sections (extended balance sheet): When calculating WACC with/without pension assets, beta is calculated in order to determine firm risk. For debt and FI investments, beta is always zero. How come? As FI is an investable asset class, it must be included in the market PF or be considered riskless. If it is not riskless (which it isn’t), it must have beta unequal to zero.
- What is the duration of a stock? Obviously, a bank stock must have at least some sensitivity to interest rate changes. So, how do beta and duration actually relate?
- From the risk material, we know that exposure to either stock indices (=beta) or interest rates (=duration) can be synthetically created. If you want market exposure: Synthesize cash from bonds (=reduce duration to 0), and buy stock index futures (= increase beta). If you want interest rate exposure: Synthesize cash from equity (= reduce beta to 0), buy bond futures (= increase duration). This part of the curriculum thus assumes that equity does not have duration and bonds do not have beta.
- From the economics material, it is recommended to invest in bonds during economic downturns (higher market risk, lower interest rates), and in equity during (beginning) upturns (lower market risk premium, increasing interest rates). From CAPM, the return of an asset = interest rate + beta * market risk premium. So, equity and debt (or beta and interest rate sensitivity) are not considered independent, isolated concepts, but somehow put into relation with each other.
As I (hopefully) move towards completing the CFA program, I feel totally retarded by asking the following extremely basic questions that this whole post boils down to:
1. Does equity have duration? Or is it just (close to) 0? In that case, it would be considered totally independent of interest rate movements.
2. Do bonds have beta? Or is it just (close to) 0? In that case, it would be considered a riskless asset.
3. Is there a straight-forward relationship (formula) between leverage of a firm and beta? I.e. if beta = 2 and D/E = 1.0, the amount of debt is doubled (by issuing new bonds), what is beta?
4. Is there an economic relationship between the level of interest rates and the return on the market portfolio, and between return on euqity and debt?
I would be grateful for comments. Somehow I cannot connect the dots. Thanks, OA
 
1. In practice, equity has duration. For CFA purposes, it’s generally safe to ignore the interest rate effects on equity portfolios. In my experience, they formulate the problems in such a way that you don’t have to worry about it, or they will simply tell you what the interest rate effect ended up doing.
2. You are right that if you take “the Market Portfolio” seriously, bonds do have beta. However, in these problems, beta is usually measured relative to an equity index rather than the true market portfolio. The correlation between bonds and stocks in the world market does tend to be low (about +0.2) but it is not zero. If you remember that bonds tend to have a substantially lower SD (reflecting lower risk) than stocks, then you’ll see that bond betas relative to a stock index are in fact very small.
3. Firm stock beta has two interacting components: 1) business risk - which is about the variability of operating profits - and sometimes called “asset beta”, and 2) financial risk - which is about how much leverage you have. Basically, debt “magnifies” the business risk. IIRC, stock beta is basically (asset beta)*[1 + D/E]
4. In general, lower interest rates ought to generate higher market portfolio returns, but I think there are lots of interacting parts (lower interest rates may get companies to lever up more, interacting with increased consumption, etc.). I don’t know of a simple equation combining the two.
 
you raise some very interesting points
here’s my take -
yes there probably is some relationship - they’re similar measures of risk - duration to interest rates, and beta to systematic non-diversifiable market moves - and interest rates and systematic market moves are obviously not uncorrelated. (probably distinct relationships for the real rate and also for the inflation component)
But as far as L3 goes:
1. we change duration of a bond portfolio (and/or convert it from and to synthetic cash/bonds) by using bond futures/fwds/swaps
2. we change beta of a stock portfolio (and/or convert it from and to synthetic cash/stock) by using equity futures/fwds/swaps
3. where there is a mixed portfolio with stocks and bonds in it, the tables (eg in past exams) show the beta of the mixed portfolio as the beta of just the stock portion, and they show the duration of the mixed portfolio as the duration of the bond portion.
4. beta of liabilties comes up in the Merton paper (reading 22) - where beta of debt is always assumed to be 0 (even the PBO debt has beta of 0).
5. when situations involve interaction of national markets, they tend to separate just the duration or stock bits and deal with them in isolation - eg when determining the impact of a foreign bond (with a foreign duration in it’s local market) on the duration of a domestic investor, you simply take the foreign bond duration in it’s local market * country beta * weight in the domestic portfolio. So the foreign country market beta does come into play, but in just a linear sense.
so in my limited view of life for the purposes of L3 - in my small brain I have separated beta and duration as 2 distinct concepts to be dealt with separately.
 
I’d support null&nuller’s position here. For CFA exam purposes, you can think of duration and beta as noninteracting.
I think part of the reason that equity duration isn’t a big part of the equity portfolio management is that if interest rates drop, that will make almost all stocks rise because businesses like low-interest rate environments (for one, it usually lowers WACC). However, the cumulative total of all these effects will just make the market index rise. When that happens, the equity duration effect will reflect back into regular stocks through their beta to the market index. So in some ways, beta incorporates interest rate risk in the stock market world.
 
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