Correlations between the, MYR, AUD, USD and EUR - a qualitative assessment

Of late, the US Dollar (USD) has been falling against the Euro (EUR). In the past days, the USD has broken all-time-low records against the Euro several times. Interestingly, the Australian Dollar (AUD) strengthened markedly with respect to the Malaysian Ringgit (MYR) over this period of time.



The Euro strengthens against the US Dollar, while the Australian Dollar strengthens against the Malaysian Ringgit

This observation suggests that it is plausible that the value of the AUD is closely connected to the EUR, and the value of the MYR is closely connected to the USD. If this is indeed the case, then the fall of the USD against the EUR will be partially mirrored by the MYR decreasing in value against the AUD.

To investigate this, the MYR will be compared with the USD and EUR to find which currency is more closely connected to the MYR, and the AUD will also be compared to the USD and EUR.



Data presentation

Average daily exchange rate data from the past 5 years are used. All data are normalised by dividing the daily exchange rate by the average exchange rate of the previous 100 days. The normalisation operation (dividing by an average) will bring all values close to 1, so that different exchange rates can be compared easily on the same scale. Effectively, the normalisation process highlights the percentage change in exchange rate.

The selection of 100 day moving average is mostly arbitrary, but the reasoning is so that gradual trends occurring over time scales of 3 months or more are not shown, but changes occurring at smaller timescales are shown.



Data comparison approach

To find the correlation of the MYR against the USD and EUR, normalised exchange rates between all three currencies will be plotted on the same graph.

In the limiting case, where the MYR is exactly correlated to the USD, the USD-EUR rate will be correlated to the MYR-EUR rate. In this limiting case, the normalised MYR is identical to the normalised USD, thus the normalised MYR-EUR and normalised USD-EUR exchange rates are identical.

In the past, the MYR was pegged to the USD at a fixed rate of MYR 3.8 = USD 1. This represents the limiting scenario described above. The figure below shows a comparison of exchange rates between September 2003 and September 2005, and the USD-EUR exchange rate is exactly the same as the MYR-EUR rate in that period.



Echange rates between the Malaysian Ringgit, Euro and US Dollar for the period between Sept 2003 to Sept 2005.

In summary, if the MYR is closely correlated to the USD, then MYR-EUR and USD-EUR exchange rates are closely correlated because there is little difference between MYR and USD.


Data analysis - MYR

The following graph shows the MYR, EUR and USD exchange rates for the past 830 days (an arbitrary choice). The exchange rates have been chosen so that the USD-EUR forms the basis of comparison. If the MYR is closely related to the USD, then the MYR-EUR rates should resemble the USD-EUR rates.

On the other hand, if the MYR is closely related to the EUR, then the USD-MYR rates should resemble the USD-EUR rates.



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Exchange rates between the Malaysian Ringgit, Euro and US Dollar for the period between July 2005 to Sept 2007

In the earlier half of the period graphed, the USD-EUR and MYR-EUR rates are very similar, suggesting that the USD and MYR are still strongly correlated. Closer to the present, near the end of the graphed period, the correlation is less obvious. However, the MYR is still closer to the USD than to the EUR.



Data analysis - AUD

The following graph shows the AUD, EUR and USD exchange rates for the past 830 days (an arbitrary choice). The exchange rates have been chosen so that the USD-EUR forms the basis of comparison. If the AUD is closely related to the USD, then the AUD-EUR rates should resemble the USD-EUR rates.

On the other hand, if the AUD is closely related to the EUR, then the USD-AUD rates should resemble the USD-EUR rates.



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Exchange rates between the Australian Dollar, Euro and US Dollar for the period between July 2005 to Sept 2007

From the 830 days graphed here, the AUD follows the EUR in a fairly consistent manner. Thus the AUD is much closely correlated to the EUR than to the USD.


Concluding remarks

From the analysis done above, it is shown qualitatively that the MYR is closely correlated to the USD, and that the AUD is closely correlated to the EUR. A change of the USD-EUR exchange rate will be reflected in a similar change in the MYR-AUD exchange rate.


Additional information

Exchange rates
5-year data for normalised rates used in this analysis can viewed for:
MYR, EUR, USD
AUD, EUR, USD

Experiments in off-camera lighting strategies

After reading Strobist, I was sufficiently inspired to try out a few of the techniques discussed. With no flashgun of my own yet (a Nikon SB-25 will be shipped from Germany within the next few days; a wireless flash trigger is expected in a similar timeframe), I had to make do with a halogen incandescent reading lamp as my secondary light (instead of a strobe).

For this exercise, I borrowed a tabletop figurine from the housemate. A few of these figurines were rather scantily clad or posed in interesting positions. In the interest of photography and concentration, I picked the one with the most clothes on.


Side light:



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The main light source is ambient light, in this case several overhead lights. This ambient lighting was very even and gave very little shadows, as the image above shows.




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A diffuse secondary light was added on the left side of the camera, consisting of a halogen lamp’s beam directed to a sheet of white paper. The side light helps give depth to the image. In particular, a gentle shadow line is created along the subject’s face and sides facing the left are brighter. In this example, the texture of the clothes is clearly shown.

Note that by adding a sidelight to the subject, the subject is now illuminated by ambient lighting and the secondary light. However, the background is only lit by ambient light and is darker than the subject. Allowing the subject to be correctly exposed means the background is now darker than before.


Back light/ separation light:



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The main light in this case is also ambient light, but this time there happens to be a strong light overhead (note the shadows cast by the hair on the forehead).




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A secondary light was added on the left side behind the subject, located just outside the camera frame. This backlighting is visible on the left boundaries of the subject, effectively drawing a bright outline against the dark background.




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A reflector constructed of aluminium foil was placed on the right side of the subject, located just outside the camera frame. This creates additional outlining on the right side.

Adding the backlight and backlight reflector effectively separates the subject from a dark background. A dark subject can then be photographed in a dark environment while allowing the subject to stand out from its environment.

Deriving the lower bound of option prices without explicit invocation of the no-arbitrage argument

The method of derivation presented here takes advantage of (in)equality of value rather than assuming no-arbitrage

Price of a call option, c
Price of a put option, p
Strike price of option, K
Time to expiry, T
Current market price of underlying commodity, S
Risk-free continuously compounded interest rate, r




On the expiry date, someone who holds a call option and some cash equal to the strike price (K) can choose to buy the commodity at the fixed price K regardless of the market price (S) of the commodity. Obviously, if the market price turns out to be higher than the strike price, the buyer gets to buy at a lower price, which means the option is now worth a bundle of money. On the other hand, if the strike price is higher than market price, the holder will not exercise the option and the option is worth nothing.


Therefore, it follows that the call option plus K in cash is at least as valuable as the commodity’s market price (S). On the expiry date, the value of a call option obeys the following correlation:


If it is not yet the expiry date, then the sum of money K should be suitably discounted to reflect the time to expiry and the interest rate. However, S is not discounted as it represents the commodity itself, not a sum of money that can be invested.

The above equation can be modified to suit a time before expiry:


This is the lower bound of a call option’s price.


***

The lower bound for a put option can be derived in a similar fashion.


On the expiry date, someone who holds a put option and the commodity can choose to sell the commodity at the strike price (K) regardless of the market price (S) of the commodity.

Therefore, it follows that the put option plus the commodity is at least as valuable as the strike price (K).

On the expiry date, the value of a put option obeys the following correlation:


If it is not yet the expiry date, then the sum of money K should be suitable discounted by the time to expiry and the interest rate. However, S is not discounted as it represent the commodity itself, not a sum of money that can be invested.

The above equation can be modified to suit a time before expiry:


This is the lower bound of a put option’s price.

Show Off

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The coffee machine's steam wand continues to amaze. Perhaps I've a strange attraction to manual control processes, such as manual gearboxes, cutting and sharpening, milk frothing (obviously without the frothing attachment) and side-kicks.

Lens arbitrage

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Yesterday, I acquired a new lens (yes I know, again). A Tamron 28mm f/2.8 on Pentax screw mount, which is very close to my Meyer-Optik Görlitz Lydith 30mm f/3.5 (2 mm wider, half a stop faster). Finished in brushed aluminium, the lens is quite a striking difference to all those black rubber-clad tubes out there.




Cyclops

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The shop did not know the mount for the lens, and it was generically labelled as “fits most SLR cameras”. It’s actually a Tamron Adaptall 2 system which can be adapted to fit Canon, Nikon, Pentax K, Minolta, Konica and M42 mounts. This particular specimen came with the M42 screw mount, but someone made a mess and thought it was a T-mount (like the M42, the T-mount has 42 mm screw threads but with different thread widths). And the secondary market for T-mount lenses is very small.

Hence, it was cheap.




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So, I now have an arbitrage opportunity. Essentially, buy low sell high with no value adding.

Also, my position appears to be hedged by means of a put option (because I managed to get the salesperson to wrongly ‘confirm’ that the lens is a T-mount, I have a leeway in returning the thing if the need arises).

I didn’t know specialist knowledge can be so useful...




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The rear of the lens showing the M42 mount



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The workings of the Adaptall 2 mechanism with the Adaptall - M42 adapter removed

See my newly expanded vocabulary? I’ve been levelling up.

Two overused phrases:

• Cute
• Morbid curiosity (and its derivatives)

***

In the distance, in black hole within Galaxy 0402+379 slowly devours an orbiting star. Material from the star’s surface is slowly shredded off and angrily churned in high energy accretion disc. The material gradually gets drawn towards the black hole, finally disappearing beyond the event horizon. The black hole emits a violent, continuous burp in the form of two high energy relativistic jets along the poles of the accretion disc.

Meanwhile, I seem to have acquired a syndrome of sorts. I feel slightly depressed when weekends and weekday evenings pass without any productivity. This is probably a good thing in terms of my quest to work through that 5 kilograms of light reading material, but it does indicate that something is not quite right under the surface.

More disturbingly, there appears to be a positive correlation between this syndrome’s absence and the presence of certain events. If this correlation is strong, the implications are not good- perhaps an underlying emotional instability or psychological black hole.

But in the meantime, faark it; I will go back to studying corporate finance.

Photographs update

We now have a coffee machine at home. All hail caffeine.





On Reflection

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Super Takumar 50mm/1.4 with extension tubes





Silver Lining

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Hanimex 400mm/6.3 at 1/4000s, f/22, ISO 100. Note the lack of lens flare despite the sun's rather strong presence.





Swanston Street, 11.11pm

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Moonrise over Melbourne

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Angle of view: ~135°
Super Takumar 50mm/1.4

The engineer strikes back: a brief theoretical investigation in the design of vibrators (vaginal stimulation devices)

One of the housemates pointed me to this entry by Finicky Feline:

With great sadness, I gave it one last kiss and threw it in the dustbin.
My brrbrrbrr, at 20 months of age, has died on me. Sputter sputter and then silence.
We had some ecstatic moments you and I.
But maybe it’s a blessing in disguise because I’ll finally need a man.

source

“She calls her thing brr brr brr!”
“Hmm, do those things pulsate?”
“Why are you asking me?”

While changing, I had a sudden flash of insight: the pulsations of a vibrator can be incorporated mechanically without the need for switching/oscillating electronics. I ran upstairs to explain to the housemate...


A commonly employed method to set up vibrations is to install a lop-sided piece of weight on a rotating shaft. For this application of pulsating vibrations, two eccentrically mounted (a fancy way of saying ‘unbalanced’) weights are required. The rotating weights are to be driven at similar but not identical speeds.

The force exerted (in the x-direction) by a rotating mass is sinusoidal. Because the two weights are rotated at slightly different speeds, the sinusoids have slightly different frequencies:


Side note:

The similar but non-identical speeds of these rotating weights can be easily designed by the use of gears. Shaft A (which holds mass a) can be connected to shaft B (which holds mass b) by a pair of gears. In the examples used here, the gear on shaft A has 22 teeth; the gear on shaft B has 20 teeth. A motor driving any of these shafts would drive both of them with the preset ratio of speeds.

The combined effect of sinusoids of different frequencies (but identical amplitudes) exhibits a beating trend: the vibration frequency is the average of the two vibrations, while the beating frequency is the difference between the two vibrations.



Side note:

The centripetal/centrifugal force (F) associated with an eccentric weight of mass M, eccentricity e (distance from shaft centerline to centre of mass) and rotation speed ω is of the following form:
F = M × ω / e

Given that the force amplitudes of both shafts are to be the same,
F1 = F2, and hence
M1 × ω1 / e1 = M2 × ω2 / e2

The following figure shows the combined vibration with an envelope equivalent to the frequency difference between the rotating masses:


Later, when I was washing dishes, the complication of the vibrator problem revealed itself. The vibration amplitude not only pulsates in the x direction, but also in the y direction. What’s more, the pulsations in the x-direction are out of phase with the pulsations in the y-direction.

Restricting the analysis to the x-direction gives a severely misleading picture of the vibration behavior of this hypothetical Brrbrrbrr. When observed in 2 dimensions, the behavior of the vibration is rather interesting.

The direction of vibration precesses (rotates slowly), the rate of precession being equal to the speed difference of the two rotating masses.


This is what gives the pulsations in the x and y directions. As the direction of vibration rotates to coincide with the x-direction, the amplitude of vibration is the greatest in the x-direction. When the direction of vibration is perpendicular to the x-direction, there is no amplitude in the x-direction. Hence, the x-vibration pulsates.



So it turns out that the pure pulsation I was searching for cannot be found in pairs of rotating masses. However, the pulsation can be restored by canceling vibrations in the y-direction, leaving only the x-direction to pulsate. This can be done by two pairs of rotating masses that rotate in opposite directions.


The arrangement shown above is designed so that the y-direction component of the centripetal forces are set up in opposing directions so that they contribute to a net of zero y-direction forces. But, the x-direction forces are arranged in the same direction, so that the x-direction vibration amplitude is doubled. And here, the analysis for uniaxial vibration (as presented above) can be applied, and pulsation is achieved.

Success!