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Jan. 9th, 2016

Star Wars

Spoilers ahead. The Internet has no shortage of Star Wars opinions, but Star Wars is fun to think and write about even if there's no-one reading.

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Nov. 11th, 2015

Dream closure

(There's no point to this story – it's just an unusual pair of dreams for me.)

A while ago – a year-ish perhaps, but it wasn't so remarkable at the time that I noted it down anywhere – I had a dream, possibly a recurring one, that I'd gone back to university. Studying for a coursework Master's, I was enrolled in a geostatistics course, the sort of course that I was lecturing in real life. And I was totally overwhelmed by it. I couldn't keep up with the assignments, and as the weeks went by, it became clearer and clearer to me that I was going to fail. I dropped out, my self-confidence crushed, having lost what is perhaps my best skill, namely passing maths-heavy university courses.

Those feelings of total inadequacy passed soon after waking up, and I hadn't thought back to those dreams since long after waking up after the last of them. Then last night I dreamt that I'd taken on tutoring a third-year maths course in neural networks, despite only knowing about one sixth of the lecture material. (I'm working through a book on the subject over at my .com.) I was sure that I'd be able to learn the content well enough as the course progressed to teach it.

I can't remember if I was awake or still dreaming when I recalled my dreamt coursework failure of a year ago, though given the strength of the emotions involved, it was surely while still dreaming. It was as though, by becoming a tutor for material that I didn't yet know and being sure that I'd do a good job at it, I'd redeemed myself for giving up on the geostats course. A small moment of strongly felt triumph, a heavy weight lifted from my shoulders. I woke up happy.
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Jan. 12th, 2015

Brief notes on partially franked dividends

On a recent trip to Brisbane I was having dinner with a group of old friends, and I realised that we had become incredibly boring people who talked about superannuation, the stock market, and so forth. In this post, I set out some notes on the taxation of partially franked dividends; I think it is relevant to at least two people, author included.

(I worked this algebra out today, not financial advice, may only apply to Australia, may not even be correct though I think it is, etc.)

You own shares in a company. The company pays out a dividend to its shareholders, without having paid company tax on it first. In this case, we call the dividend unfranked, and you pay tax on it according to your marginal income tax rate (probably 32.5% or 37%). If your marginal income tax rate is ti, and the dividend is D, then you'll owe the tax office ti*D.

The more complicated case is if the company pays its company tax on the dividend before giving it to shareholders. If the company tax has been paid in full, then the dividend you get is fully franked. The key points are:

  • The ATO taxes, at your marginal income tax rate, the imputed full value of the dividend before the company tax was paid on it (the grossed-up dividend).
  • You get credits for the tax that the company has already paid on the grossed-up dividend, so that the tax isn't paid twice.


Algebra should make this clearer (if not, there are heaps of explanations on Google). Let tc be the company tax rate (30%). Let Df be the franked dividend, i.e., what you receive. Let Dg be the grossed-up dividend, i.e., what the tax is being imposed on. We have

(1 - tc)*Dg = Df.

More generally, the dividend may be only partially franked. Let f be the fraction of the dividend which is fully franked. Then

(1 - f*tc)*Dg = Df.         (*)

The total amount of tax the ATO wants is ti*Dg. The company's already paid f*tc*Dg, so you owe

tax_owing = ti*Dg - f*tc*Dg = Dg*(ti - f*tc).

(If this quantity is negative, then the tax office owes you money, and this can either turn into a tax refund or offset some other tax.)

It is more useful to use (*) to work out how much tax you owe as a function of the dividend that you receive:

tax_owing = Df * (ti - f*tc) / (1 - f*tc).

Plugging some numbers in: if the dividend is fully franked, then f=1. Say ti = 37.5%, and tc = 30%. Then you owe the ATO (37.5% - 30%) / (1 - 30%) = 10.7% of the dividend you receive.

In the last couple of years, Vanguard's VHY fund has been giving distributions (which I gather is called a different term to 'dividend' because the distribution comprises lots of individual dividends from all the companies in the fund) around 70% franked. Plugging in f = 0.7, we get (37.5% - 0.7*30%) / (1 - 0.7*30%) = 20.9%. So about a fifth of the distribution you get will go to the tax office.

(This remains the case even if you set up an automatic re-investment plan; the ATO treats it as though you received the income in the form of partially franked dividends, then bought more shares with it. The income is taxed.)

We can use this to estimate the effective returns from a fund. From the above link, VHY's growth since inception has been an annualised average of 13% p.a., comprising 7.1% p.a. growth in the unit price and 5.9% p.a. in distributions. Since about a fifth of the latter is eaten up by tax, the effective return has been a bit under 12% p.a. rather than 13%.

My eyeballing of the table in that PDF file suggests that taking a percentage point off the returns is a decent rule of thumb for working this out, at least if you're in my tax bracket. The forecast growth is 8%, so I'll interpret that as around 7%. (And remember that as a 95% confidence interval, the forecast for a single year is more like (8 +/- 25)%.)

Dec. 31st, 2014

Fixing relative notation in music

I've been learning a tiny little bit of music theory – major scales and chords and so on – and I would like to change everyone's use of relative notation.

The usual way of writing relative notes in a scale is 1, 2, 3, 4, 5, 6, 7. In C major, this would correspond to C, D, E, F, G, A, B. Chords are usually written in Roman numerals, with capital letters for major chords and lower-case letters for minor chords: I, ii, iii, IV, V, vi, viio for C, Dm, Em, F, G, Am, Bdim.

The first problem I see with this is when we want to describe secondary chords like V/V, "five of five": we temporarily go to the major scale of the 5, and extract the V chord from that scale. In C major, the V chord is a G major; in the G major scale, the 5 is a D, so the V/V is a D major chord.

I expect that people who work with these things regularly work these out as quickly as I can do my times tables, hopping between scales with ease. But I would like to work things out in terms of modular arithmetic. In the case above, things appear to work out: there are eight notes in an octave, 5 + 5 = 10, and 10 (mod 8) = 2, and D is the 2 in the C scale.

But this breaks down if we want the V/ii chord: 5 + 2 = 7, but the ii is D, and the 5 in the D scale is an A, not a B.

The mathematically-inclined may have already spotted at least one of the mistakes in the above reasoning. There are seven different notes in the scale, so we should be working modulo 7, not modulo 8. The second mistake is with the notation: the scale should start with zero, not 1.

To do the calculation properly, we need to first subtract 1 after doing the addition. So, V/V is 5 + 5 - 1 (mod 7) = 2. And V/ii is 2 + 5 - 1 (mod 7) = 6. It works.

Having to subtract the 1 is really annoying though, and the special case of ending on a 7 (e.g., V/iii which becomes zero mod 7) needs to be handled. A better scale would be

0, 1, 2, 3, 4, 5, 6

with chords
O, i, ii, III, IV, v, vio.

Then the normal-notation V/V becomes a IV/IV, and can be calculated as 4 + 4 (mod 7) = 1, the D major chord. And a normal-notation V/ii becomes a IV/i, and can be calculated as 1 + 4 (mod 7) = 5, the A major chord.

This is much cleaner, and the only minor issue is a roman numeral for the zero , which I wrote above as a letter O.

Taking into account how little music theory I know, I figure my proposal is somewhere about as optimistic as my suggestion for question marks.
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Nov. 10th, 2014

Diamantina Drover

(A longer post than is likely warranted for not hearing lyrics correctly, but perhaps it's worth it if overseas readers (both of you) haven't heard the song before.)

I can't specifically remember it, but I think I first heard Diamantina Drover in the form of John Williamson's cover version on his album Mallee Boy. My parents had a few Williamson albums and that was definitely one of them. I recall later learning the lyrics in a primary school music class; I can't remember actually singing it, but we must have. Whether we sang something closer to Redgum's original or Williamson's more compactly arranged cover, I don't know, but certainly it's Williamson's version which remains one of my favourite songs (of any genre, and certainly within Australian folk).

The song's narrator tells us about how he moved from Sydney a decade ago to become a cattle drover. The first verse and chorus end with "I won't be back till the drovin's done." The last verse ends with "I won't be back when the drovin's done", a change kept in the final chorus as well.

I was at the YouTube video of the Williamson version of this song, and started reading the comments.

Musically i like Johns version but he should have stuck to the red gum lyrics. Changing that one little word at the end takes out all the impact and kind off the whole point to the song.

?????

I knew when reading this that the commenter was referring to the till/when switch, saying that Williamson had sung 'till' in every case instead of changing to 'when'. And I straight-up didn't believe this, until I played through the YouTube video, hearing "till the drovin's done" always and never hearing "when the drovin's done". I figured I couldn't have misheard the lyrics so consistently over so many years, so I checked the album version that I own... and I had misheard.

I'd obviously been taught the Redgum lyrics, and they'd stuck with me through many dozens of plays of John Williamson's version. Perhaps, many years ago, I noticed that John didn't make the till/when switch – having written this post I now recall noticing this sometime around 2000, listening to the song on cassette in Dad's car. But I'd long forgotten about it, if that is actually a genuine memory and not something I'm inventing for myself.

Someone not hearing lyrics right is hardly earth-shattering news, but this one feels much more interesting to me than others.

Having thought about this, I think a compromise would actually improve the lyrics even further. The final verse should switch to 'when', as in the original. But the final chorus should stay as 'till' – the final verse then would have that brief moment of raw honesty, before the narrator slips back into the lie that one day he'll move back to Sydney.
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