Consider a position consisting of a 300,000 investment in gold and a 500,000 investment in sil

Consider a position consisting of a 300,000 investment in...

Key Concepts

Diversification Benefit

Diversification benefit refers to the reduction in overall portfolio risk achieved by combining assets that do not perfectly correlate with each other. By spreading investments across different assets, particularly those with low or moderate correlations, the portfolio's total risk is lowered compared to the weighted sum of individual asset risks, demonstrating the value of diversification in risk management.

Portfolio Variance and Covariance

Portfolio variance analysis involves calculating the overall risk of a portfolio by considering both the individual asset volatilities and the covariances between asset returns. The covariance terms account for how the returns of different assets move in relation to each other, influencing the total portfolio risk and illustrating the benefits or drawbacks of asset combinations.

Correlation

Correlation measures the degree to which two asset returns move together, quantitatively expressed between -1 and 1. In portfolio risk calculations, the correlation coefficient plays a crucial role in estimating the combined risk of assets, where a lower or negative correlation can lead to significant diversification benefits by reducing overall portfolio variance.

Volatility Scaling (Square Root of Time Rule)

The square root of time rule is a principle used to scale volatility estimates for different time horizons. If daily volatility is known, the volatility for a longer time period can be approximated by multiplying the daily volatility by the square root of the number of days. This assumption is valid under the condition of independently and identically distributed returns.

Value at Risk (VaR)

Value at Risk is a statistical measure used in finance to quantify the level of financial risk within a portfolio over a specific time frame, given a certain confidence level. It represents the maximum expected loss under normal market conditions, allowing investors and risk managers to assess potential losses and make informed decisions about risk exposure.

Transcript

00:01 So we've got $450 ,000 to invest, and we've got an option of investing in something that returns 6 % or something that returns 10%.

00:11 So we're going to define x as the amount we invest invested in the 6 % category, and y is the amount invested in the 10 % return investment.

00:36 Those are return on investments.

00:42 And we've been specified, or it's been specified, that we have to invest at least in the 6 % investment, at least 250 % of the investment, or 225k.

00:56 So we can say x has to be greater than or equal to $225 ,000.

01:07 We want to have at least 50 % invested there.

01:10 And y has to be greater than or equal to 25%.

01:15 Or a quarter of the investment money, which is, again, we have a $450k total, so that would be $112k.

01:32 And we know that the amount we make from this is really going to be the profit or the amount return on the investment is going to be the amount we invest in 6 % times 1 .06, plus the amount we invest in, in the 10 % times 1 .1.

01:55 So the return on the investment, and we'll write this as roi, total is equal to 1 .06 times x plus 1 .1 times y.

02:16 And we know that the total x plus y can't be more than 450 because that's how much we have to invest.

02:27 So if this is our x -axis, this is our y -axis? we know that somewhere over here, say 225, we have to be, x has to be greater than 225.

02:48 So we have to be somewhere in this region.

02:53 X has to be greater than that value.

02:59 And we know also that y has to be greater than 112.

03:05 So we could draw a line there somewhere in here.

03:13 And y has to be greater than that.

03:21 So we're really talking about the intersection of those regions is somewhere in here.

03:26 But the other requirement we have is x plus y is equal to 450.

03:30 Well, what does that look like from an equation standpoint? we could write it in y equals mx plus b, something we're used to.

03:38 Y equals negative x plus 450.

03:45 So let's extend our y -axis a little bit here.

03:48 And let's imagine it looking something like that.

03:54 So that's basically a slope of negative 1 with a y intercept of 450.

04:03 450 there.

04:04 So that's pretty clear.

04:06 Y intercept.

04:08 But we also know this point down here is that when y equals 0, x is going to have to equal 450.

04:16 That's the x intercept right there.

04:22 So to figure out what the optimum investment is, we need to look at the intersection points of these three investments or these three extreme situations...

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