ask Dcifrths...well, anything...about finance/mkts/ports that is.

[HP]

Okay I had a highly theoretical, probably not practical at all, thought the other day. Feel free to ignore if it's pointless to discuss

Assume:

a perfectly efficient money market
it is possible to borrow and lend cash at the same interest rate, in the US and in Europe
there will always be a minimum amount variance in the USD/EUR
the USD and EUR will always exist

Okay so basically we buy 100 USD worth of EUR today, and put the EUR in the bank earning interest.

We buy back USD once the exchange rate is such that we make ten times as much USD than we would have if we had just put it into a US bank account to begin with

Now, if I've understood random walk theory correctly, if there will always be a minimum amount of variance, and it's always a random walk, the chance the exchange rate will eventually hit our target (so we can make ten times as much) is 100%. It may take a number generations and our decedents may be the only ones profiting, but we don't mind we are nice people

This seems counterintuitive - it's like we are beating the perfectly efficient market. Thoughts?

[DcifrThs]

your example assumes that the price of the exchange rate and the interest rates are completely independent. they are highly intertwined.

so think about what that means if the interest rates are the same and the exchange rate drops...it is kind of like saying that their economies are chugging along at the same pace yet the relative pricing of their currencies jumped out of whack. what could cause that? massive swings in domestic consumption or other huuuuge swings of domestic/int'l economic preferences (that don't affect the other country proportionally). but what do those swings do to growth? they'd have to have NO AFFECT for the interest rates to be locked together at that exact level, OR they would have to affect the two countries in the exact same way in perfect proportion to keep the relative rates in lock step at a different level.

that is clearly not possible.

further, the market will make sure the actual example never happens for another main reason: the market mechanism will move the prices back to lock step via selling the higher exchange rate and buying the lower one b/c the IRs are preciesely the same.

other problems with your exmaple are that you're assuming that you will earn above the compound interest return every time you wait for the 10:1 payoff. but if that 10:1 payoff takes over T years, where T is the number of years investing at the risk free rate of interest earns you 1000% compound returns. if the 10:1 payoff takes longer than T years then you've "lost" money since you would have done better by doing nothing.

so what is the probability that it takes less than T years...well now we're in fantasy land with the normal distribution as the descriptor of financial markets (i assume in your exmaple that the random walk = normal distribution).

further, if EVERYTHING else in your example actually worked...if the market is efficient, then the probability that it takes fewer than T years to hit 10:1 will be such that you don't earn an expected excess return.

so basically the example is nothing more than an interesting thought. it was good though b/c it actually took me a little bit to figure out.

thanks,
Barron

[Zygote]

In a prior debate we had the discussion of diversification came up.

Im still trying to understand the position you've taken here as this seems to evade all the logic in my head. I recently had a similar debate with my roommate, a CFA in training, who takes the same position as you but he has thus far failed to do a satisfactory job of defending the theory.

Can you please try explain to me where my reasoning is wrong specifically? I know you already gave some reasoning but i dont understand how that proved the thesis that through portfolio management, owning multiple assets will increase returns without increasing risk or will decrease risk without sacrificing returns compared to choosing the most optimal single investment in the portfolio.

Here is why i think this is impossible. If you have two possible investments, regardless of structure, and their sharpe ratios are different from one another, then one asset must have a better sharpe ratio than the other.

If this is so, the only way combining these assets can improve risk to performance is if you compare the worse of the two assets to the combination of the two assets. However, if you compare the other way around you will see that is better to use limited funds towards only the best of the basket.

Im not against diversification but i think the reasons for doing so should be clear:

-Minimize risk at the expense of returns.
-Isolate exposure

[DcifrThs]

[ QUOTE ]
In a prior debate we had the discussion of diversification came up.

Im still trying to understand the position you've taken here as this seems to evade all the logic in my head. I recently had a similar debate with my roommate, a CFA in training, who takes the same position as you but he has thus far failed to do a satisfactory job of defending the theory.

Can you please try explain to me where my reasoning is wrong specifically? I know you already gave some reasoning but i dont understand how that proved the thesis that through portfolio management, owning multiple assets will increase returns without increasing risk or will decrease risk without sacrificing returns compared to choosing the most optimal single investment in the portfolio.

Here is why i think this is impossible. If you have two possible investments, regardless of structure, and their sharpe ratios are different from one another, then one asset must have a better sharpe ratio than the other.

If this is so, the only way combining these assets can improve risk to performance is if you compare the worse of the two assets to the combination of the two assets. However, if you compare the other way around you will see that is better to use limited funds towards only the best of the basket.

Im not against diversification but i think the reasons for doing so should be clear:

-Minimize risk at the expense of returns.
-Isolate exposure

[/ QUOTE ]
the easiest way to explain it is in the institutional investor sense.

institutional investors have access to leverage. leverage is the key that makes diversification far more valuable than it is without leverage.

in your example, you have 2 investments, A & B.

A's SR = .3 (say a global stock portfolio)
B's SR = .25 (say a US bond allocation)

their correlation is say 50%.

it is trivial to prove that a weighting scheme [wA wB] where wB >0 can increase the risk adjusted return of the portfolio vs. the portfolio where wB=0. the reason is that the introduction of B at the level wB will reduce more risk than it takes away from returns to a point (where wB then has become too large and takes away more returns than risk it decreases).

now, if you have access to leverage, you can choose a risk level for asset B and leverage it to hit the exact return of A.

for example, say the global stock index investment has a 12% volatility and 4% returns.

the bond fund on the other hand has 8% vol and 2% returns. you can leverage the bond allocation 2:1 and hit the same return target without altering the bond allocation's sharpe ratio nor its correlational benefits in a portfolio construction context.

now, a portfolio [wA wB] can be optimized such that you aim to maximize your risk adjusted returns and then use leverage to hit an absolute return target.

the key here is that your drawdowns will be far less severe and fewer in # while at the same time, you will have the exact same level of returns as you did with wB=0.

so with leverage, it is clearly the case that diversification is far better than isolated investments in the highest returning investment.

now, in terms of an individual investor (you or me), we don't have the same access to leverage, but we do hav access to diversification.

if your concern is solely maximizing yoru returns, with absolutely no care for risk, then why not simply invest in emerging market tech stocks?

why? well the reason is because risk has a cost. interms of CAPM (just a starting point to discuss this), the risk aversion parameter tells the portfolio constructor how much return must be acheived in order to justify a one unit increase in risk.

in other words, if i can acheive a return of 20% with 60% volatility annualized, how much return would i give up to get that risk down to 45%?

clearly a 60% vol, even if i generates 20% returns (higher than the expected returns on a well diversified portfolio for an individual), introduces cost into the portfolio.

one cost is that drawdowns reduce the compounding effect for investments. a big drawdown will reduce the base from which you can earn that compound return. a portfolio with the lowest drawdowns will be proportionally better than a portfolio with the largest returns and bigger vol from a risk adjusted return standpoint.

the other cost is in terms of time frame. if your horizon is, say 20 years, with a 60% vol, the chance of you ending on a big drawdown is far higher than with a 30% vol which could wipe out years of realized returns at the wrong time. this is where those "lifecycle" funds get the idea to gradually shift to lower income assets.

so for an individual, it is correct to say that to minimize risk, you must give up returns...but if the returns you give up are lower than the cost of the higher risk (given your "risk aversion parameter), then that risk reduction is clearly worthwhile. you should, obviously then, reduce risk until the marginal changes of the risk/return tradeoff are equal (where the next unit of risk reduction costs too much in terms of sacrificed returns relative to your risk aversion parameter).

for an institutional investor, however, that has access to hedge funds to run leveraged portfolios for them for 50bps in total fees at SRs of .70 and then simply pick the level of risk they want, diversification is clearly, no question better.

hope this helps,
Barron

[Zygote]

[ QUOTE ]

so for an individual, it is correct to say that to minimize risk, you must give up returns...but if the returns you give up are lower than the cost of the higher risk (given your "risk aversion parameter), then that risk reduction is clearly worthwhile. you should, obviously then, reduce risk until the marginal changes of the risk/return tradeoff are equal (where the next unit of risk reduction costs too much in terms of sacrificed returns relative to your risk aversion parameter).

[/ QUOTE ]

I agree with this entirely.

[ QUOTE ]
for an institutional investor, however, that has access to hedge funds to run leveraged portfolios for them for 50bps in total fees at SRs of .70 and then simply pick the level of risk they want, diversification is clearly, no question better.

[/ QUOTE ]

What i dont understand is why dont they only stick to the less volatile leveraged assets if that's the case? Why doesnt all their money just go there?

[DcifrThs]

[ QUOTE ]
[ QUOTE ]

so for an individual, it is correct to say that to minimize risk, you must give up returns...but if the returns you give up are lower than the cost of the higher risk (given your "risk aversion parameter), then that risk reduction is clearly worthwhile. you should, obviously then, reduce risk until the marginal changes of the risk/return tradeoff are equal (where the next unit of risk reduction costs too much in terms of sacrificed returns relative to your risk aversion parameter).

[/ QUOTE ]

I agree with this entirely.

[ QUOTE ]
for an institutional investor, however, that has access to hedge funds to run leveraged portfolios for them for 50bps in total fees at SRs of .70 and then simply pick the level of risk they want, diversification is clearly, no question better.

[/ QUOTE ]

What i dont understand is why dont they only stick to the less volatile leveraged assets if that's the case? Why doesnt all their money just go there?

[/ QUOTE ]

because the diversificaiton reduces drawdowns without any reduction in returns via leverage. less volatile leveraged assets would be like TIPS, short treasuries etc. but those correlate negatively (or zero), and lowly-medium with equities, emerging marke equities etc.

that is the main thing. if you can reduce risk via ANY jiggling in the portfolio, you can use leverage to hit the return target you want.

maximizing the sharpe ratio for an institutional investor with access to leverage is the only concern. a portfolio of lowly volatile asset classes doesn't accomplish this goal.

Barron

[Zygote]

[ QUOTE ]
because the diversificaiton reduces drawdowns without any reduction in returns via leverage.

[/ QUOTE ]

Im saying lets assume the portfolio starts with only the leveraged assets. Does adding the global stock index to the portfolio reduce risk without sacrificing returns or add returns without increasing risk, risk aversion reasons aside?

Is it because they use one security to get leverage on another security?

[DcifrThs]

[ QUOTE ]
[ QUOTE ]
because the diversificaiton reduces drawdowns without any reduction in returns via leverage.

[/ QUOTE ]

Im saying lets assume the portfolio starts with only the leveraged assets. Does adding the global stock index to the portfolio reduce risk without sacrificing returns or add returns without increasing risk, risk aversion reasons aside?

[/ QUOTE ]

the addition of a global stock index w/ a SR of .3 4% returns 12% vol (to a portfolio of TIPS/ST treasuries leveraged to hit 4% returns) reduces risk without decreasing returns. this is because it is 0% correlated with TIPS and between 40-60% correlated with the ST treasuries.

you can then leverage this portfolio (with a better sharpe ratio) to hit any risk level/return level you want.

further, you should also then add EMD, commodities (you can delever these through CCFs) etc. such that the overall sharpe ratio continues to increase. your portfolio will then also be protected against all economic environments (high inflation low growth, high inflation high growth, low inflation low growth, low inflation high growth) and will have the lowest drawdowns.

that is the proof of diversification you were looking for i think. the key though is you need access to leverage.

Barron

[Zygote]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
because the diversificaiton reduces drawdowns without any reduction in returns via leverage.

[/ QUOTE ]

Im saying lets assume the portfolio starts with only the leveraged assets. Does adding the global stock index to the portfolio reduce risk without sacrificing returns or add returns without increasing risk, risk aversion reasons aside?

[/ QUOTE ]

the addition of a global stock index w/ a SR of .3 4% returns 12% vol (to a portfolio of TIPS/ST treasuries leveraged to hit 4% returns) reduces risk without decreasing returns. this is because it is 0% correlated with TIPS and between 40-60% correlated with the ST treasuries.

you can then leverage this portfolio (with a better sharpe ratio) to hit any risk level/return level you want.

further, you should also then add EMD, commodities (you can delever these through CCFs) etc. such that the overall sharpe ratio continues to increase. your portfolio will then also be protected against all economic environments (high inflation low growth, high inflation high growth, low inflation low growth, low inflation high growth) and will have the lowest drawdowns.

that is the proof of diversification you were looking for i think. the key though is you need access to leverage.

Barron

[/ QUOTE ]

I think im understanding what you're saying. Ive always understood the benefits of diversifying to minimize risk but have yet to understand the benefits of increasing ev.

I agree that leverage seems to be the key, but more specifically is it the fact that you use one security to get leverage on the other security that really ties this all together?

[DcifrThs]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
because the diversificaiton reduces drawdowns without any reduction in returns via leverage.

[/ QUOTE ]

Im saying lets assume the portfolio starts with only the leveraged assets. Does adding the global stock index to the portfolio reduce risk without sacrificing returns or add returns without increasing risk, risk aversion reasons aside?

[/ QUOTE ]

the addition of a global stock index w/ a SR of .3 4% returns 12% vol (to a portfolio of TIPS/ST treasuries leveraged to hit 4% returns) reduces risk without decreasing returns. this is because it is 0% correlated with TIPS and between 40-60% correlated with the ST treasuries.

you can then leverage this portfolio (with a better sharpe ratio) to hit any risk level/return level you want.

further, you should also then add EMD, commodities (you can delever these through CCFs) etc. such that the overall sharpe ratio continues to increase. your portfolio will then also be protected against all economic environments (high inflation low growth, high inflation high growth, low inflation low growth, low inflation high growth) and will have the lowest drawdowns.

that is the proof of diversification you were looking for i think. the key though is you need access to leverage.

Barron

[/ QUOTE ]

I think im saying what you're saying. Ive always understood the benefits of diversifying to minimize risk but have yet to understand the benefits of increasing ev.

I agree that leverage seems to be the key, but more specifically is it the fact that you use one security to get leverage on the other security that really ties this all together?

[/ QUOTE ]

in a manner of speaking, yes...if you define repos or whatever you use to generate leverage as "a security to get leverage on another"... derivative securities definitely are the key.

institutional investors vastly underutilize lowly correlated asset classes and then bump up their risk target via leverage.

hope this helps,
Barron